neuper@37906
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1 |
(* theory collecting all knowledge
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neuper@37906
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2 |
(predicates 'is_rootEq_in', 'is_sqrt_in', 'is_ratEq_in')
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neuper@37906
|
3 |
for PolynomialEquations.
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wneuper@59592
|
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alternative dependencies see @{theory "Isac_Knowledge"}
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neuper@37906
|
5 |
created by: rlang
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neuper@37906
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6 |
date: 02.07
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neuper@37906
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changed by: rlang
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neuper@37906
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last change by: rlang
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neuper@37906
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9 |
date: 03.06.03
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neuper@37954
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10 |
(c) by Richard Lang, 2003
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neuper@37906
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*)
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neuper@37906
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12 |
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neuper@37954
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theory PolyEq imports LinEq RootRatEq begin
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neuper@37906
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neuper@37906
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15 |
(*-------------------- rules -------------------------------------------------*)
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walther@60242
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(* type real enforced by op " \<up> " *)
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neuper@52148
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axiomatization where
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walther@60242
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cancel_leading_coeff1: "Not (c =!= 0) ==> (a + b*bdv + c*bdv \<up> 2 = 0) =
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walther@60242
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(a/c + b/c*bdv + bdv \<up> 2 = 0)" and
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walther@60242
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cancel_leading_coeff2: "Not (c =!= 0) ==> (a - b*bdv + c*bdv \<up> 2 = 0) =
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walther@60242
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(a/c - b/c*bdv + bdv \<up> 2 = 0)" and
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walther@60242
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cancel_leading_coeff3: "Not (c =!= 0) ==> (a + b*bdv - c*bdv \<up> 2 = 0) =
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walther@60242
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(a/c + b/c*bdv - bdv \<up> 2 = 0)" and
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neuper@37906
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24 |
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walther@60242
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cancel_leading_coeff4: "Not (c =!= 0) ==> (a + bdv + c*bdv \<up> 2 = 0) =
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walther@60242
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(a/c + 1/c*bdv + bdv \<up> 2 = 0)" and
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walther@60242
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cancel_leading_coeff5: "Not (c =!= 0) ==> (a - bdv + c*bdv \<up> 2 = 0) =
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walther@60242
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(a/c - 1/c*bdv + bdv \<up> 2 = 0)" and
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walther@60242
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cancel_leading_coeff6: "Not (c =!= 0) ==> (a + bdv - c*bdv \<up> 2 = 0) =
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walther@60242
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(a/c + 1/c*bdv - bdv \<up> 2 = 0)" and
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neuper@37906
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walther@60242
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cancel_leading_coeff7: "Not (c =!= 0) ==> ( b*bdv + c*bdv \<up> 2 = 0) =
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walther@60242
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( b/c*bdv + bdv \<up> 2 = 0)" and
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walther@60242
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cancel_leading_coeff8: "Not (c =!= 0) ==> ( b*bdv - c*bdv \<up> 2 = 0) =
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walther@60242
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( b/c*bdv - bdv \<up> 2 = 0)" and
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neuper@37906
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36 |
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walther@60242
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37 |
cancel_leading_coeff9: "Not (c =!= 0) ==> ( bdv + c*bdv \<up> 2 = 0) =
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walther@60242
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( 1/c*bdv + bdv \<up> 2 = 0)" and
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walther@60242
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cancel_leading_coeff10:"Not (c =!= 0) ==> ( bdv - c*bdv \<up> 2 = 0) =
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walther@60242
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( 1/c*bdv - bdv \<up> 2 = 0)" and
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neuper@37906
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walther@60242
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cancel_leading_coeff11:"Not (c =!= 0) ==> (a + b*bdv \<up> 2 = 0) =
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walther@60242
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(a/b + bdv \<up> 2 = 0)" and
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walther@60242
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cancel_leading_coeff12:"Not (c =!= 0) ==> (a - b*bdv \<up> 2 = 0) =
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walther@60242
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(a/b - bdv \<up> 2 = 0)" and
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walther@60242
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cancel_leading_coeff13:"Not (c =!= 0) ==> ( b*bdv \<up> 2 = 0) =
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walther@60242
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( bdv \<up> 2 = 0/b)" and
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neuper@37906
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walther@60242
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complete_square1: "(q + p*bdv + bdv \<up> 2 = 0) =
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walther@60242
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(q + (p/2 + bdv) \<up> 2 = (p/2) \<up> 2)" and
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walther@60242
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complete_square2: "( p*bdv + bdv \<up> 2 = 0) =
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walther@60242
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( (p/2 + bdv) \<up> 2 = (p/2) \<up> 2)" and
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walther@60242
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complete_square3: "( bdv + bdv \<up> 2 = 0) =
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walther@60242
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( (1/2 + bdv) \<up> 2 = (1/2) \<up> 2)" and
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neuper@37906
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walther@60242
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complete_square4: "(q - p*bdv + bdv \<up> 2 = 0) =
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walther@60242
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(q + (p/2 - bdv) \<up> 2 = (p/2) \<up> 2)" and
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walther@60242
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complete_square5: "(q + p*bdv - bdv \<up> 2 = 0) =
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walther@60242
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(q + (p/2 - bdv) \<up> 2 = (p/2) \<up> 2)" and
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neuper@37906
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walther@60242
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square_explicit1: "(a + b \<up> 2 = c) = ( b \<up> 2 = c - a)" and
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walther@60242
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square_explicit2: "(a - b \<up> 2 = c) = (-(b \<up> 2) = c - a)" and
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neuper@37906
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walther@60242
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(*bdv_explicit* required type constrain to real in --- (-8 - 2*x + x \<up> 2 = 0), by rewriting ---*)
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neuper@52148
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bdv_explicit1: "(a + bdv = b) = (bdv = - a + (b::real))" and
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neuper@52148
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bdv_explicit2: "(a - bdv = b) = ((-1)*bdv = - a + (b::real))" and
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neuper@52148
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bdv_explicit3: "((-1)*bdv = b) = (bdv = (-1)*(b::real))" and
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neuper@37906
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neuper@52148
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plus_leq: "(0 <= a + b) = ((-1)*b <= a)"(*Isa?*) and
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neuper@52148
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minus_leq: "(0 <= a - b) = ( b <= a)"(*Isa?*) and
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neuper@37906
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wneuper@59370
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(*-- normalise --*)
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neuper@37906
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(*WN0509 compare LinEq.all_left "[|Not(b=!=0)|] ==> (a=b) = (a+(-1)*b=0)"*)
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neuper@52148
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all_left: "[|Not(b=!=0)|] ==> (a = b) = (a - b = 0)" and
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walther@60242
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makex1_x: "a\<up>1 = a" and
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neuper@52148
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real_assoc_1: "a+(b+c) = a+b+c" and
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neuper@52148
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real_assoc_2: "a*(b*c) = a*b*c" and
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neuper@37906
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neuper@37906
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(* ---- degree 0 ----*)
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neuper@52148
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d0_true: "(0=0) = True" and
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neuper@52148
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d0_false: "[|Not(bdv occurs_in a);Not(a=0)|] ==> (a=0) = False" and
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neuper@37906
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(* ---- degree 1 ----*)
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neuper@37983
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d1_isolate_add1:
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neuper@52148
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"[|Not(bdv occurs_in a)|] ==> (a + b*bdv = 0) = (b*bdv = (-1)*a)" and
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neuper@37983
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d1_isolate_add2:
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neuper@52148
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"[|Not(bdv occurs_in a)|] ==> (a + bdv = 0) = ( bdv = (-1)*a)" and
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neuper@37983
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d1_isolate_div:
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neuper@52148
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"[|Not(b=0);Not(bdv occurs_in c)|] ==> (b*bdv = c) = (bdv = c/b)" and
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neuper@37906
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(* ---- degree 2 ----*)
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neuper@37983
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d2_isolate_add1:
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walther@60242
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"[|Not(bdv occurs_in a)|] ==> (a + b*bdv \<up> 2=0) = (b*bdv \<up> 2= (-1)*a)" and
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neuper@37983
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d2_isolate_add2:
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walther@60242
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"[|Not(bdv occurs_in a)|] ==> (a + bdv \<up> 2=0) = ( bdv \<up> 2= (-1)*a)" and
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neuper@37983
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d2_isolate_div:
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walther@60242
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"[|Not(b=0);Not(bdv occurs_in c)|] ==> (b*bdv \<up> 2=c) = (bdv \<up> 2=c/b)" and
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neuper@42394
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walther@60242
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d2_prescind1: "(a*bdv + b*bdv \<up> 2 = 0) = (bdv*(a +b*bdv)=0)" and
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walther@60242
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d2_prescind2: "(a*bdv + bdv \<up> 2 = 0) = (bdv*(a + bdv)=0)" and
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walther@60242
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d2_prescind3: "( bdv + b*bdv \<up> 2 = 0) = (bdv*(1+b*bdv)=0)" and
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walther@60242
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d2_prescind4: "( bdv + bdv \<up> 2 = 0) = (bdv*(1+ bdv)=0)" and
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neuper@37906
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(* eliminate degree 2 *)
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neuper@37906
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(* thm for neg arguments in sqroot have postfix _neg *)
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neuper@37983
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d2_sqrt_equation1: "[|(0<=c);Not(bdv occurs_in c)|] ==>
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walther@60242
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(bdv \<up> 2=c) = ((bdv=sqrt c) | (bdv=(-1)*sqrt c ))" and
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t@42197
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d2_sqrt_equation1_neg:
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walther@60242
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"[|(c<0);Not(bdv occurs_in c)|] ==> (bdv \<up> 2=c) = False" and
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walther@60242
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d2_sqrt_equation2: "(bdv \<up> 2=0) = (bdv=0)" and
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walther@60242
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d2_sqrt_equation3: "(b*bdv \<up> 2=0) = (bdv=0)"
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neuper@52148
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axiomatization where (*AK..if replaced by "and" we get errors:
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t@42203
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exception PTREE "nth _ []" raised
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t@42203
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(line 783 of "/usr/local/isabisac/src/Tools/isac/Interpret/ctree.sml"):
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t@42203
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'fun nth _ [] = raise PTREE "nth _ []"'
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t@42203
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and
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t@42203
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exception Bind raised
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t@42203
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(line 1097 of "/usr/local/isabisac/test/Tools/isac/Frontend/interface.sml"):
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t@42203
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'val (Form f, tac, asms) = pt_extract (pt, p);' *)
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walther@60242
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(* WN120315 these 2 thms need "::real", because no " \<up> " constrains type as
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neuper@42394
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required in test --- rls d2_polyeq_bdv_only_simplify --- *)
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neuper@52148
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d2_reduce_equation1: "(bdv*(a +b*bdv)=0) = ((bdv=0)|(a+b*bdv=(0::real)))" and
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neuper@42394
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d2_reduce_equation2: "(bdv*(a + bdv)=0) = ((bdv=0)|(a+ bdv=(0::real)))"
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neuper@52148
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neuper@52148
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axiomatization where (*..if replaced by "and" we get errors:
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t@42203
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exception PTREE "nth _ []" raised
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t@42203
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(line 783 of "/usr/local/isabisac/src/Tools/isac/Interpret/ctree.sml"):
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t@42203
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'fun nth _ [] = raise PTREE "nth _ []"'
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t@42203
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and
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t@42203
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exception Bind raised
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t@42203
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(line 1097 of "/usr/local/isabisac/test/Tools/isac/Frontend/interface.sml"):
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t@42203
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'val (Form f, tac, asms) = pt_extract (pt, p);' *)
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walther@60273
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d2_pqformula1: "[|0<=p \<up> 2 - 4*q|] ==> (q+p*bdv+ bdv \<up> 2=0) =
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walther@60242
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((bdv= (-1)*(p/2) + sqrt(p \<up> 2 - 4*q)/2)
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walther@60242
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| (bdv= (-1)*(p/2) - sqrt(p \<up> 2 - 4*q)/2))" and
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walther@60242
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d2_pqformula1_neg: "[|p \<up> 2 - 4*q<0|] ==> (q+p*bdv+ bdv \<up> 2=0) = False" and
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walther@60242
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d2_pqformula2: "[|0<=p \<up> 2 - 4*q|] ==> (q+p*bdv+1*bdv \<up> 2=0) =
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walther@60242
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((bdv= (-1)*(p/2) + sqrt(p \<up> 2 - 4*q)/2)
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walther@60242
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| (bdv= (-1)*(p/2) - sqrt(p \<up> 2 - 4*q)/2))" and
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walther@60242
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d2_pqformula2_neg: "[|p \<up> 2 - 4*q<0|] ==> (q+p*bdv+1*bdv \<up> 2=0) = False" and
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walther@60242
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d2_pqformula3: "[|0<=1 - 4*q|] ==> (q+ bdv+ bdv \<up> 2=0) =
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neuper@37954
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((bdv= (-1)*(1/2) + sqrt(1 - 4*q)/2)
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neuper@52148
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| (bdv= (-1)*(1/2) - sqrt(1 - 4*q)/2))" and
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walther@60242
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d2_pqformula3_neg: "[|1 - 4*q<0|] ==> (q+ bdv+ bdv \<up> 2=0) = False" and
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walther@60242
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d2_pqformula4: "[|0<=1 - 4*q|] ==> (q+ bdv+1*bdv \<up> 2=0) =
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neuper@37954
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((bdv= (-1)*(1/2) + sqrt(1 - 4*q)/2)
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neuper@52148
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| (bdv= (-1)*(1/2) - sqrt(1 - 4*q)/2))" and
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walther@60242
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d2_pqformula4_neg: "[|1 - 4*q<0|] ==> (q+ bdv+1*bdv \<up> 2=0) = False" and
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walther@60242
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d2_pqformula5: "[|0<=p \<up> 2 - 0|] ==> ( p*bdv+ bdv \<up> 2=0) =
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walther@60242
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((bdv= (-1)*(p/2) + sqrt(p \<up> 2 - 0)/2)
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walther@60242
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| (bdv= (-1)*(p/2) - sqrt(p \<up> 2 - 0)/2))" and
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t@42203
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149 |
(* d2_pqformula5_neg not need p^2 never less zero in R *)
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walther@60402
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150 |
d2_pqformula6: " ( p*bdv+1*bdv \<up> 2=0) =
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walther@60242
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((bdv= (-1)*(p/2) + sqrt(p \<up> 2 - 0)/2)
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walther@60242
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| (bdv= (-1)*(p/2) - sqrt(p \<up> 2 - 0)/2))" and
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neuper@37906
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(* d2_pqformula6_neg not need p^2 never less zero in R *)
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walther@60402
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154 |
d2_pqformula7: " ( bdv+ bdv \<up> 2=0) =
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neuper@37954
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((bdv= (-1)*(1/2) + sqrt(1 - 0)/2)
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neuper@52148
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156 |
| (bdv= (-1)*(1/2) - sqrt(1 - 0)/2))" and
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neuper@37906
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157 |
(* d2_pqformula7_neg not need, because 1<0 ==> False*)
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walther@60402
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158 |
d2_pqformula8: " ( bdv+1*bdv \<up> 2=0) =
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neuper@37954
|
159 |
((bdv= (-1)*(1/2) + sqrt(1 - 0)/2)
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neuper@52148
|
160 |
| (bdv= (-1)*(1/2) - sqrt(1 - 0)/2))" and
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neuper@37906
|
161 |
(* d2_pqformula8_neg not need, because 1<0 ==> False*)
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neuper@37983
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162 |
d2_pqformula9: "[|Not(bdv occurs_in q); 0<= (-1)*4*q|] ==>
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walther@60242
|
163 |
(q+ 1*bdv \<up> 2=0) = ((bdv= 0 + sqrt(0 - 4*q)/2)
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neuper@52148
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| (bdv= 0 - sqrt(0 - 4*q)/2))" and
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neuper@37983
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165 |
d2_pqformula9_neg:
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walther@60242
|
166 |
"[|Not(bdv occurs_in q); (-1)*4*q<0|] ==> (q+ 1*bdv \<up> 2=0) = False" and
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neuper@37983
|
167 |
d2_pqformula10:
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walther@60242
|
168 |
"[|Not(bdv occurs_in q); 0<= (-1)*4*q|] ==> (q+ bdv \<up> 2=0) =
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neuper@37906
|
169 |
((bdv= 0 + sqrt(0 - 4*q)/2)
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neuper@52148
|
170 |
| (bdv= 0 - sqrt(0 - 4*q)/2))" and
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neuper@37983
|
171 |
d2_pqformula10_neg:
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walther@60242
|
172 |
"[|Not(bdv occurs_in q); (-1)*4*q<0|] ==> (q+ bdv \<up> 2=0) = False" and
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neuper@37983
|
173 |
d2_abcformula1:
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walther@60242
|
174 |
"[|0<=b \<up> 2 - 4*a*c|] ==> (c + b*bdv+a*bdv \<up> 2=0) =
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walther@60242
|
175 |
((bdv=( -b + sqrt(b \<up> 2 - 4*a*c))/(2*a))
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walther@60242
|
176 |
| (bdv=( -b - sqrt(b \<up> 2 - 4*a*c))/(2*a)))" and
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neuper@37983
|
177 |
d2_abcformula1_neg:
|
walther@60242
|
178 |
"[|b \<up> 2 - 4*a*c<0|] ==> (c + b*bdv+a*bdv \<up> 2=0) = False" and
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neuper@37983
|
179 |
d2_abcformula2:
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walther@60242
|
180 |
"[|0<=1 - 4*a*c|] ==> (c+ bdv+a*bdv \<up> 2=0) =
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neuper@37906
|
181 |
((bdv=( -1 + sqrt(1 - 4*a*c))/(2*a))
|
neuper@52148
|
182 |
| (bdv=( -1 - sqrt(1 - 4*a*c))/(2*a)))" and
|
neuper@37983
|
183 |
d2_abcformula2_neg:
|
walther@60242
|
184 |
"[|1 - 4*a*c<0|] ==> (c+ bdv+a*bdv \<up> 2=0) = False" and
|
neuper@37983
|
185 |
d2_abcformula3:
|
walther@60242
|
186 |
"[|0<=b \<up> 2 - 4*1*c|] ==> (c + b*bdv+ bdv \<up> 2=0) =
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walther@60242
|
187 |
((bdv=( -b + sqrt(b \<up> 2 - 4*1*c))/(2*1))
|
walther@60242
|
188 |
| (bdv=( -b - sqrt(b \<up> 2 - 4*1*c))/(2*1)))" and
|
neuper@37983
|
189 |
d2_abcformula3_neg:
|
walther@60242
|
190 |
"[|b \<up> 2 - 4*1*c<0|] ==> (c + b*bdv+ bdv \<up> 2=0) = False" and
|
neuper@37983
|
191 |
d2_abcformula4:
|
walther@60242
|
192 |
"[|0<=1 - 4*1*c|] ==> (c + bdv+ bdv \<up> 2=0) =
|
neuper@37906
|
193 |
((bdv=( -1 + sqrt(1 - 4*1*c))/(2*1))
|
neuper@52148
|
194 |
| (bdv=( -1 - sqrt(1 - 4*1*c))/(2*1)))" and
|
neuper@37983
|
195 |
d2_abcformula4_neg:
|
walther@60242
|
196 |
"[|1 - 4*1*c<0|] ==> (c + bdv+ bdv \<up> 2=0) = False" and
|
neuper@37983
|
197 |
d2_abcformula5:
|
walther@60242
|
198 |
"[|Not(bdv occurs_in c); 0<=0 - 4*a*c|] ==> (c + a*bdv \<up> 2=0) =
|
neuper@37906
|
199 |
((bdv=( 0 + sqrt(0 - 4*a*c))/(2*a))
|
neuper@52148
|
200 |
| (bdv=( 0 - sqrt(0 - 4*a*c))/(2*a)))" and
|
neuper@37983
|
201 |
d2_abcformula5_neg:
|
walther@60242
|
202 |
"[|Not(bdv occurs_in c); 0 - 4*a*c<0|] ==> (c + a*bdv \<up> 2=0) = False" and
|
neuper@37983
|
203 |
d2_abcformula6:
|
walther@60242
|
204 |
"[|Not(bdv occurs_in c); 0<=0 - 4*1*c|] ==> (c+ bdv \<up> 2=0) =
|
neuper@37906
|
205 |
((bdv=( 0 + sqrt(0 - 4*1*c))/(2*1))
|
neuper@52148
|
206 |
| (bdv=( 0 - sqrt(0 - 4*1*c))/(2*1)))" and
|
neuper@37983
|
207 |
d2_abcformula6_neg:
|
walther@60242
|
208 |
"[|Not(bdv occurs_in c); 0 - 4*1*c<0|] ==> (c+ bdv \<up> 2=0) = False" and
|
neuper@37983
|
209 |
d2_abcformula7:
|
walther@60242
|
210 |
"[|0<=b \<up> 2 - 0|] ==> ( b*bdv+a*bdv \<up> 2=0) =
|
walther@60242
|
211 |
((bdv=( -b + sqrt(b \<up> 2 - 0))/(2*a))
|
walther@60242
|
212 |
| (bdv=( -b - sqrt(b \<up> 2 - 0))/(2*a)))" and
|
neuper@37906
|
213 |
(* d2_abcformula7_neg not need b^2 never less zero in R *)
|
neuper@37983
|
214 |
d2_abcformula8:
|
walther@60242
|
215 |
"[|0<=b \<up> 2 - 0|] ==> ( b*bdv+ bdv \<up> 2=0) =
|
walther@60242
|
216 |
((bdv=( -b + sqrt(b \<up> 2 - 0))/(2*1))
|
walther@60242
|
217 |
| (bdv=( -b - sqrt(b \<up> 2 - 0))/(2*1)))" and
|
neuper@37906
|
218 |
(* d2_abcformula8_neg not need b^2 never less zero in R *)
|
neuper@37983
|
219 |
d2_abcformula9:
|
walther@60242
|
220 |
"[|0<=1 - 0|] ==> ( bdv+a*bdv \<up> 2=0) =
|
neuper@37906
|
221 |
((bdv=( -1 + sqrt(1 - 0))/(2*a))
|
neuper@52148
|
222 |
| (bdv=( -1 - sqrt(1 - 0))/(2*a)))" and
|
neuper@37906
|
223 |
(* d2_abcformula9_neg not need, because 1<0 ==> False*)
|
neuper@37983
|
224 |
d2_abcformula10:
|
walther@60242
|
225 |
"[|0<=1 - 0|] ==> ( bdv+ bdv \<up> 2=0) =
|
neuper@37906
|
226 |
((bdv=( -1 + sqrt(1 - 0))/(2*1))
|
neuper@52148
|
227 |
| (bdv=( -1 - sqrt(1 - 0))/(2*1)))" and
|
neuper@37906
|
228 |
(* d2_abcformula10_neg not need, because 1<0 ==> False*)
|
neuper@37906
|
229 |
|
t@42203
|
230 |
|
neuper@37906
|
231 |
(* ---- degree 3 ----*)
|
neuper@37983
|
232 |
d3_reduce_equation1:
|
walther@60242
|
233 |
"(a*bdv + b*bdv \<up> 2 + c*bdv \<up> 3=0) = (bdv=0 | (a + b*bdv + c*bdv \<up> 2=0))" and
|
neuper@37983
|
234 |
d3_reduce_equation2:
|
walther@60242
|
235 |
"( bdv + b*bdv \<up> 2 + c*bdv \<up> 3=0) = (bdv=0 | (1 + b*bdv + c*bdv \<up> 2=0))" and
|
neuper@37983
|
236 |
d3_reduce_equation3:
|
walther@60242
|
237 |
"(a*bdv + bdv \<up> 2 + c*bdv \<up> 3=0) = (bdv=0 | (a + bdv + c*bdv \<up> 2=0))" and
|
neuper@37983
|
238 |
d3_reduce_equation4:
|
walther@60242
|
239 |
"( bdv + bdv \<up> 2 + c*bdv \<up> 3=0) = (bdv=0 | (1 + bdv + c*bdv \<up> 2=0))" and
|
neuper@37983
|
240 |
d3_reduce_equation5:
|
walther@60242
|
241 |
"(a*bdv + b*bdv \<up> 2 + bdv \<up> 3=0) = (bdv=0 | (a + b*bdv + bdv \<up> 2=0))" and
|
neuper@37983
|
242 |
d3_reduce_equation6:
|
walther@60242
|
243 |
"( bdv + b*bdv \<up> 2 + bdv \<up> 3=0) = (bdv=0 | (1 + b*bdv + bdv \<up> 2=0))" and
|
neuper@37983
|
244 |
d3_reduce_equation7:
|
walther@60242
|
245 |
"(a*bdv + bdv \<up> 2 + bdv \<up> 3=0) = (bdv=0 | (1 + bdv + bdv \<up> 2=0))" and
|
neuper@37983
|
246 |
d3_reduce_equation8:
|
walther@60242
|
247 |
"( bdv + bdv \<up> 2 + bdv \<up> 3=0) = (bdv=0 | (1 + bdv + bdv \<up> 2=0))" and
|
neuper@37983
|
248 |
d3_reduce_equation9:
|
walther@60242
|
249 |
"(a*bdv + c*bdv \<up> 3=0) = (bdv=0 | (a + c*bdv \<up> 2=0))" and
|
neuper@37983
|
250 |
d3_reduce_equation10:
|
walther@60242
|
251 |
"( bdv + c*bdv \<up> 3=0) = (bdv=0 | (1 + c*bdv \<up> 2=0))" and
|
neuper@37983
|
252 |
d3_reduce_equation11:
|
walther@60242
|
253 |
"(a*bdv + bdv \<up> 3=0) = (bdv=0 | (a + bdv \<up> 2=0))" and
|
neuper@37983
|
254 |
d3_reduce_equation12:
|
walther@60242
|
255 |
"( bdv + bdv \<up> 3=0) = (bdv=0 | (1 + bdv \<up> 2=0))" and
|
neuper@37983
|
256 |
d3_reduce_equation13:
|
walther@60242
|
257 |
"( b*bdv \<up> 2 + c*bdv \<up> 3=0) = (bdv=0 | ( b*bdv + c*bdv \<up> 2=0))" and
|
neuper@37983
|
258 |
d3_reduce_equation14:
|
walther@60242
|
259 |
"( bdv \<up> 2 + c*bdv \<up> 3=0) = (bdv=0 | ( bdv + c*bdv \<up> 2=0))" and
|
neuper@37983
|
260 |
d3_reduce_equation15:
|
walther@60242
|
261 |
"( b*bdv \<up> 2 + bdv \<up> 3=0) = (bdv=0 | ( b*bdv + bdv \<up> 2=0))" and
|
neuper@37983
|
262 |
d3_reduce_equation16:
|
walther@60242
|
263 |
"( bdv \<up> 2 + bdv \<up> 3=0) = (bdv=0 | ( bdv + bdv \<up> 2=0))" and
|
neuper@37983
|
264 |
d3_isolate_add1:
|
walther@60242
|
265 |
"[|Not(bdv occurs_in a)|] ==> (a + b*bdv \<up> 3=0) = (b*bdv \<up> 3= (-1)*a)" and
|
neuper@37983
|
266 |
d3_isolate_add2:
|
walther@60242
|
267 |
"[|Not(bdv occurs_in a)|] ==> (a + bdv \<up> 3=0) = ( bdv \<up> 3= (-1)*a)" and
|
neuper@37983
|
268 |
d3_isolate_div:
|
walther@60242
|
269 |
"[|Not(b=0);Not(bdv occurs_in a)|] ==> (b*bdv \<up> 3=c) = (bdv \<up> 3=c/b)" and
|
neuper@37983
|
270 |
d3_root_equation2:
|
walther@60242
|
271 |
"(bdv \<up> 3=0) = (bdv=0)" and
|
neuper@37983
|
272 |
d3_root_equation1:
|
walther@60242
|
273 |
"(bdv \<up> 3=c) = (bdv = nroot 3 c)" and
|
neuper@37906
|
274 |
|
neuper@37906
|
275 |
(* ---- degree 4 ----*)
|
neuper@37906
|
276 |
(* RL03.FIXME es wir nicht getestet ob u>0 *)
|
neuper@37989
|
277 |
d4_sub_u1:
|
walther@60242
|
278 |
"(c+b*bdv \<up> 2+a*bdv \<up> 4=0) =
|
walther@60242
|
279 |
((a*u \<up> 2+b*u+c=0) & (bdv \<up> 2=u))" and
|
neuper@37906
|
280 |
|
neuper@37906
|
281 |
(* ---- 7.3.02 von Termorder ---- *)
|
neuper@37906
|
282 |
|
neuper@52148
|
283 |
bdv_collect_1: "l * bdv + m * bdv = (l + m) * bdv" and
|
neuper@52148
|
284 |
bdv_collect_2: "bdv + m * bdv = (1 + m) * bdv" and
|
neuper@52148
|
285 |
bdv_collect_3: "l * bdv + bdv = (l + 1) * bdv" and
|
neuper@37906
|
286 |
|
neuper@37906
|
287 |
(* bdv_collect_assoc0_1 "l * bdv + m * bdv + k = (l + m) * bdv + k"
|
neuper@37906
|
288 |
bdv_collect_assoc0_2 "bdv + m * bdv + k = (1 + m) * bdv + k"
|
neuper@37906
|
289 |
bdv_collect_assoc0_3 "l * bdv + bdv + k = (l + 1) * bdv + k"
|
neuper@37906
|
290 |
*)
|
neuper@52148
|
291 |
bdv_collect_assoc1_1: "l * bdv + (m * bdv + k) = (l + m) * bdv + k" and
|
neuper@52148
|
292 |
bdv_collect_assoc1_2: "bdv + (m * bdv + k) = (1 + m) * bdv + k" and
|
neuper@52148
|
293 |
bdv_collect_assoc1_3: "l * bdv + (bdv + k) = (l + 1) * bdv + k" and
|
neuper@38030
|
294 |
|
neuper@52148
|
295 |
bdv_collect_assoc2_1: "k + l * bdv + m * bdv = k + (l + m) * bdv" and
|
neuper@52148
|
296 |
bdv_collect_assoc2_2: "k + bdv + m * bdv = k + (1 + m) * bdv" and
|
neuper@52148
|
297 |
bdv_collect_assoc2_3: "k + l * bdv + bdv = k + (l + 1) * bdv" and
|
neuper@37906
|
298 |
|
neuper@37906
|
299 |
|
walther@60242
|
300 |
bdv_n_collect_1: "l * bdv \<up> n + m * bdv \<up> n = (l + m) * bdv \<up> n" and
|
walther@60242
|
301 |
bdv_n_collect_2: " bdv \<up> n + m * bdv \<up> n = (1 + m) * bdv \<up> n" and
|
walther@60242
|
302 |
bdv_n_collect_3: "l * bdv \<up> n + bdv \<up> n = (l + 1) * bdv \<up> n" (*order!*) and
|
neuper@37906
|
303 |
|
walther@60358
|
304 |
bdv_n_collect_assoc1_1: "l * bdv \<up> n + (m * bdv \<up> n + k) = (l + m) * bdv \<up> n + k" and
|
walther@60242
|
305 |
bdv_n_collect_assoc1_2: "bdv \<up> n + (m * bdv \<up> n + k) = (1 + m) * bdv \<up> n + k" and
|
walther@60242
|
306 |
bdv_n_collect_assoc1_3: "l * bdv \<up> n + (bdv \<up> n + k) = (l + 1) * bdv \<up> n + k" and
|
neuper@37906
|
307 |
|
walther@60242
|
308 |
bdv_n_collect_assoc2_1: "k + l * bdv \<up> n + m * bdv \<up> n = k +(l + m) * bdv \<up> n" and
|
walther@60242
|
309 |
bdv_n_collect_assoc2_2: "k + bdv \<up> n + m * bdv \<up> n = k + (1 + m) * bdv \<up> n" and
|
walther@60242
|
310 |
bdv_n_collect_assoc2_3: "k + l * bdv \<up> n + bdv \<up> n = k + (l + 1) * bdv \<up> n" and
|
neuper@37906
|
311 |
|
neuper@37906
|
312 |
(*WN.14.3.03*)
|
neuper@52148
|
313 |
real_minus_div: "- (a / b) = (-1 * a) / b" and
|
neuper@38030
|
314 |
|
neuper@52148
|
315 |
separate_bdv: "(a * bdv) / b = (a / b) * (bdv::real)" and
|
walther@60242
|
316 |
separate_bdv_n: "(a * bdv \<up> n) / b = (a / b) * bdv \<up> n" and
|
neuper@52148
|
317 |
separate_1_bdv: "bdv / b = (1 / b) * (bdv::real)" and
|
walther@60242
|
318 |
separate_1_bdv_n: "bdv \<up> n / b = (1 / b) * bdv \<up> n"
|
neuper@37906
|
319 |
|
wneuper@59472
|
320 |
ML \<open>
|
neuper@37954
|
321 |
val PolyEq_prls = (*3.10.02:just the following order due to subterm evaluation*)
|
walther@60358
|
322 |
Rule_Set.append_rules "PolyEq_prls" Rule_Set.empty [
|
walther@60358
|
323 |
\<^rule_eval>\<open>ident\<close> (Prog_Expr.eval_ident "#ident_"),
|
walther@60358
|
324 |
\<^rule_eval>\<open>matches\<close> (Prog_Expr.eval_matches "#matches_"),
|
walther@60358
|
325 |
\<^rule_eval>\<open>lhs\<close> (Prog_Expr.eval_lhs ""),
|
walther@60358
|
326 |
\<^rule_eval>\<open>rhs\<close> (Prog_Expr.eval_rhs ""),
|
walther@60358
|
327 |
\<^rule_eval>\<open>is_expanded_in\<close> (eval_is_expanded_in ""),
|
walther@60358
|
328 |
\<^rule_eval>\<open>is_poly_in\<close> (eval_is_poly_in ""),
|
walther@60358
|
329 |
\<^rule_eval>\<open>has_degree_in\<close> (eval_has_degree_in ""),
|
walther@60358
|
330 |
\<^rule_eval>\<open>is_polyrat_in\<close> (eval_is_polyrat_in ""),
|
walther@60358
|
331 |
\<^rule_eval>\<open>HOL.eq\<close> (Prog_Expr.eval_equal "#equal_"),
|
walther@60358
|
332 |
\<^rule_eval>\<open>is_rootTerm_in\<close> (eval_is_rootTerm_in ""),
|
walther@60358
|
333 |
\<^rule_eval>\<open>is_ratequation_in\<close> (eval_is_ratequation_in ""),
|
walther@60358
|
334 |
\<^rule_thm>\<open>not_true\<close>,
|
walther@60358
|
335 |
\<^rule_thm>\<open>not_false\<close>,
|
walther@60358
|
336 |
\<^rule_thm>\<open>and_true\<close>,
|
walther@60358
|
337 |
\<^rule_thm>\<open>and_false\<close>,
|
walther@60358
|
338 |
\<^rule_thm>\<open>or_true\<close>,
|
walther@60358
|
339 |
\<^rule_thm>\<open>or_false\<close>];
|
neuper@37954
|
340 |
|
neuper@37954
|
341 |
val PolyEq_erls =
|
walther@60358
|
342 |
Rule_Set.merge "PolyEq_erls" LinEq_erls
|
walther@60358
|
343 |
(Rule_Set.append_rules "ops_preds" calculate_Rational [
|
walther@60358
|
344 |
\<^rule_eval>\<open>HOL.eq\<close> (Prog_Expr.eval_equal "#equal_"),
|
wenzelm@60297
|
345 |
\<^rule_thm>\<open>plus_leq\<close>,
|
wenzelm@60297
|
346 |
\<^rule_thm>\<open>minus_leq\<close>,
|
wenzelm@60297
|
347 |
\<^rule_thm>\<open>rat_leq1\<close>,
|
wenzelm@60297
|
348 |
\<^rule_thm>\<open>rat_leq2\<close>,
|
walther@60358
|
349 |
\<^rule_thm>\<open>rat_leq3\<close>]);
|
neuper@37954
|
350 |
|
neuper@37954
|
351 |
val PolyEq_crls =
|
walther@59852
|
352 |
Rule_Set.merge "PolyEq_crls" LinEq_crls
|
walther@60358
|
353 |
(Rule_Set.append_rules "ops_preds" calculate_Rational [
|
walther@60358
|
354 |
\<^rule_eval>\<open>HOL.eq\<close> (Prog_Expr.eval_equal "#equal_"),
|
wenzelm@60297
|
355 |
\<^rule_thm>\<open>plus_leq\<close>,
|
wenzelm@60297
|
356 |
\<^rule_thm>\<open>minus_leq\<close>,
|
wenzelm@60297
|
357 |
\<^rule_thm>\<open>rat_leq1\<close>,
|
wenzelm@60297
|
358 |
\<^rule_thm>\<open>rat_leq2\<close>,
|
wenzelm@60297
|
359 |
\<^rule_thm>\<open>rat_leq3\<close>
|
neuper@37954
|
360 |
]);
|
neuper@37954
|
361 |
|
s1210629013@55444
|
362 |
val cancel_leading_coeff = prep_rls'(
|
walther@59851
|
363 |
Rule_Def.Repeat {id = "cancel_leading_coeff", preconds = [],
|
walther@60358
|
364 |
rew_ord = ("e_rew_ord",Rewrite_Ord.e_rew_ord),
|
walther@60358
|
365 |
erls = PolyEq_erls, srls = Rule_Set.Empty, calc = [], errpatts = [],
|
walther@60358
|
366 |
rules = [
|
walther@60358
|
367 |
\<^rule_thm>\<open>cancel_leading_coeff1\<close>,
|
walther@60358
|
368 |
\<^rule_thm>\<open>cancel_leading_coeff2\<close>,
|
walther@60358
|
369 |
\<^rule_thm>\<open>cancel_leading_coeff3\<close>,
|
walther@60358
|
370 |
\<^rule_thm>\<open>cancel_leading_coeff4\<close>,
|
walther@60358
|
371 |
\<^rule_thm>\<open>cancel_leading_coeff5\<close>,
|
walther@60358
|
372 |
\<^rule_thm>\<open>cancel_leading_coeff6\<close>,
|
walther@60358
|
373 |
\<^rule_thm>\<open>cancel_leading_coeff7\<close>,
|
walther@60358
|
374 |
\<^rule_thm>\<open>cancel_leading_coeff8\<close>,
|
walther@60358
|
375 |
\<^rule_thm>\<open>cancel_leading_coeff9\<close>,
|
walther@60358
|
376 |
\<^rule_thm>\<open>cancel_leading_coeff10\<close>,
|
walther@60358
|
377 |
\<^rule_thm>\<open>cancel_leading_coeff11\<close>,
|
walther@60358
|
378 |
\<^rule_thm>\<open>cancel_leading_coeff12\<close>,
|
walther@60358
|
379 |
\<^rule_thm>\<open>cancel_leading_coeff13\<close> ],
|
walther@60358
|
380 |
scr = Rule.Empty_Prog});
|
s1210629013@55444
|
381 |
|
walther@59618
|
382 |
val prep_rls' = Auto_Prog.prep_rls @{theory};
|
wneuper@59472
|
383 |
\<close>
|
wneuper@59472
|
384 |
ML\<open>
|
s1210629013@55444
|
385 |
val complete_square = prep_rls'(
|
walther@59851
|
386 |
Rule_Def.Repeat {id = "complete_square", preconds = [],
|
walther@60358
|
387 |
rew_ord = ("e_rew_ord",Rewrite_Ord.e_rew_ord),
|
walther@60358
|
388 |
erls = PolyEq_erls, srls = Rule_Set.Empty, calc = [], errpatts = [],
|
walther@60358
|
389 |
rules = [
|
walther@60358
|
390 |
\<^rule_thm>\<open>complete_square1\<close>,
|
walther@60358
|
391 |
\<^rule_thm>\<open>complete_square2\<close>,
|
walther@60358
|
392 |
\<^rule_thm>\<open>complete_square3\<close>,
|
walther@60358
|
393 |
\<^rule_thm>\<open>complete_square4\<close>,
|
walther@60358
|
394 |
\<^rule_thm>\<open>complete_square5\<close>],
|
walther@60358
|
395 |
scr = Rule.Empty_Prog});
|
neuper@37954
|
396 |
|
s1210629013@55444
|
397 |
val polyeq_simplify = prep_rls'(
|
walther@59851
|
398 |
Rule_Def.Repeat {id = "polyeq_simplify", preconds = [],
|
walther@60358
|
399 |
rew_ord = ("termlessI",termlessI),
|
walther@60358
|
400 |
erls = PolyEq_erls,
|
walther@60358
|
401 |
srls = Rule_Set.Empty,
|
walther@60358
|
402 |
calc = [], errpatts = [],
|
walther@60358
|
403 |
rules = [
|
walther@60358
|
404 |
\<^rule_thm>\<open>real_assoc_1\<close>,
|
walther@60358
|
405 |
\<^rule_thm>\<open>real_assoc_2\<close>,
|
walther@60358
|
406 |
\<^rule_thm>\<open>real_diff_minus\<close>,
|
walther@60358
|
407 |
\<^rule_thm>\<open>real_unari_minus\<close>,
|
walther@60358
|
408 |
\<^rule_thm>\<open>realpow_multI\<close>,
|
walther@60358
|
409 |
\<^rule_eval>\<open>plus\<close> (**)(eval_binop "#add_"),
|
walther@60358
|
410 |
\<^rule_eval>\<open>minus\<close> (**)(eval_binop "#sub_"),
|
walther@60358
|
411 |
\<^rule_eval>\<open>times\<close> (**)(eval_binop "#mult_"),
|
walther@60358
|
412 |
\<^rule_eval>\<open>divide\<close> (Prog_Expr.eval_cancel "#divide_e"),
|
walther@60358
|
413 |
\<^rule_eval>\<open>sqrt\<close> (eval_sqrt "#sqrt_"),
|
wenzelm@60405
|
414 |
\<^rule_eval>\<open>realpow\<close> (**)(eval_binop "#power_"),
|
walther@60358
|
415 |
Rule.Rls_ reduce_012],
|
walther@60358
|
416 |
scr = Rule.Empty_Prog});
|
wneuper@59472
|
417 |
\<close>
|
wenzelm@60289
|
418 |
rule_set_knowledge
|
wenzelm@60286
|
419 |
cancel_leading_coeff = cancel_leading_coeff and
|
wenzelm@60286
|
420 |
complete_square = complete_square and
|
wenzelm@60286
|
421 |
PolyEq_erls = PolyEq_erls and
|
wenzelm@60286
|
422 |
polyeq_simplify = polyeq_simplify
|
wneuper@59472
|
423 |
ML\<open>
|
neuper@37954
|
424 |
|
walther@60358
|
425 |
(* the subsequent rule-sets are caused by the lack of rewriting at the time of implementation *)
|
neuper@37954
|
426 |
(* -- d0 -- *)
|
neuper@37954
|
427 |
(*isolate the bound variable in an d0 equation; 'bdv' is a meta-constant*)
|
s1210629013@55444
|
428 |
val d0_polyeq_simplify = prep_rls'(
|
walther@59851
|
429 |
Rule_Def.Repeat {id = "d0_polyeq_simplify", preconds = [],
|
walther@60358
|
430 |
rew_ord = ("e_rew_ord",Rewrite_Ord.e_rew_ord),
|
walther@60358
|
431 |
erls = PolyEq_erls,
|
walther@60358
|
432 |
srls = Rule_Set.Empty,
|
walther@60358
|
433 |
calc = [], errpatts = [],
|
walther@60358
|
434 |
rules = [
|
walther@60358
|
435 |
\<^rule_thm>\<open>d0_true\<close>,
|
walther@60358
|
436 |
\<^rule_thm>\<open>d0_false\<close>],
|
walther@60358
|
437 |
scr = Rule.Empty_Prog});
|
neuper@37954
|
438 |
|
neuper@37954
|
439 |
(* -- d1 -- *)
|
neuper@37954
|
440 |
(*isolate the bound variable in an d1 equation; 'bdv' is a meta-constant*)
|
s1210629013@55444
|
441 |
val d1_polyeq_simplify = prep_rls'(
|
walther@59851
|
442 |
Rule_Def.Repeat {id = "d1_polyeq_simplify", preconds = [],
|
walther@60358
|
443 |
rew_ord = ("e_rew_ord",Rewrite_Ord.e_rew_ord),
|
walther@60358
|
444 |
erls = PolyEq_erls,
|
walther@60358
|
445 |
srls = Rule_Set.Empty,
|
walther@60358
|
446 |
calc = [], errpatts = [],
|
walther@60358
|
447 |
rules = [
|
walther@60358
|
448 |
\<^rule_thm>\<open>d1_isolate_add1\<close>, (* a+bx=0 -> bx=-a *)
|
walther@60358
|
449 |
\<^rule_thm>\<open>d1_isolate_add2\<close>, (* a+ x=0 -> x=-a *)
|
walther@60358
|
450 |
\<^rule_thm>\<open>d1_isolate_div\<close> (* bx=c -> x=c/b *)],
|
walther@60358
|
451 |
scr = Rule.Empty_Prog});
|
walther@60358
|
452 |
\<close>
|
neuper@37954
|
453 |
|
wneuper@59472
|
454 |
subsection \<open>degree 2\<close>
|
wneuper@59472
|
455 |
ML\<open>
|
neuper@42394
|
456 |
(* isolate the bound variable in an d2 equation with bdv only;
|
neuper@42394
|
457 |
"bdv" is a meta-constant substituted for the "x" below by isac's rewriter. *)
|
s1210629013@55444
|
458 |
val d2_polyeq_bdv_only_simplify = prep_rls'(
|
walther@59857
|
459 |
Rule_Def.Repeat {id = "d2_polyeq_bdv_only_simplify", preconds = [], rew_ord = ("e_rew_ord",Rewrite_Ord.e_rew_ord),
|
walther@59851
|
460 |
erls = PolyEq_erls, srls = Rule_Set.Empty, calc = [], errpatts = [],
|
walther@60358
|
461 |
rules = [
|
walther@60358
|
462 |
\<^rule_thm>\<open>d2_prescind1\<close>, (* ax+bx^2=0 -> x(a+bx)=0 *)
|
wenzelm@60297
|
463 |
\<^rule_thm>\<open>d2_prescind2\<close>, (* ax+ x^2=0 -> x(a+ x)=0 *)
|
wenzelm@60297
|
464 |
\<^rule_thm>\<open>d2_prescind3\<close>, (* x+bx^2=0 -> x(1+bx)=0 *)
|
wenzelm@60297
|
465 |
\<^rule_thm>\<open>d2_prescind4\<close>, (* x+ x^2=0 -> x(1+ x)=0 *)
|
wenzelm@60297
|
466 |
\<^rule_thm>\<open>d2_sqrt_equation1\<close>, (* x^2=c -> x=+-sqrt(c) *)
|
wenzelm@60297
|
467 |
\<^rule_thm>\<open>d2_sqrt_equation1_neg\<close>, (* [0<c] x^2=c -> []*)
|
wenzelm@60297
|
468 |
\<^rule_thm>\<open>d2_sqrt_equation2\<close>, (* x^2=0 -> x=0 *)
|
wenzelm@60297
|
469 |
\<^rule_thm>\<open>d2_reduce_equation1\<close>,(* x(a+bx)=0 -> x=0 |a+bx=0*)
|
wenzelm@60297
|
470 |
\<^rule_thm>\<open>d2_reduce_equation2\<close>,(* x(a+ x)=0 -> x=0 |a+ x=0*)
|
walther@60358
|
471 |
\<^rule_thm>\<open>d2_isolate_div\<close>], (* bx^2=c -> x^2=c/b *)
|
walther@60358
|
472 |
scr = Rule.Empty_Prog});
|
walther@60358
|
473 |
|
walther@60358
|
474 |
(* isolate the bound variable in an d2 equation with sqrt only;
|
neuper@37954
|
475 |
'bdv' is a meta-constant*)
|
s1210629013@55444
|
476 |
val d2_polyeq_sq_only_simplify = prep_rls'(
|
walther@59851
|
477 |
Rule_Def.Repeat {id = "d2_polyeq_sq_only_simplify", preconds = [],
|
walther@60358
|
478 |
rew_ord = ("e_rew_ord",Rewrite_Ord.e_rew_ord),
|
walther@60358
|
479 |
erls = PolyEq_erls, srls = Rule_Set.Empty, calc = [], errpatts = [],
|
walther@60358
|
480 |
rules = [
|
walther@60358
|
481 |
\<^rule_thm>\<open>d2_isolate_add1\<close>,(* a+ bx^2=0 -> bx^2=(-1)a*)
|
walther@60358
|
482 |
\<^rule_thm>\<open>d2_isolate_add2\<close>, (* a+ x^2=0 -> x^2=(-1)a*)
|
walther@60358
|
483 |
\<^rule_thm>\<open>d2_sqrt_equation2\<close>, (* x^2=0 -> x=0 *)
|
walther@60358
|
484 |
\<^rule_thm>\<open>d2_sqrt_equation1\<close>, (* x^2=c -> x=+-sqrt(c)*)
|
walther@60358
|
485 |
\<^rule_thm>\<open>d2_sqrt_equation1_neg\<close>,(* [c<0] x^2=c -> x=[] *)
|
walther@60358
|
486 |
\<^rule_thm>\<open>d2_isolate_div\<close>], (* bx^2=c -> x^2=c/b*)
|
walther@60358
|
487 |
scr = Rule.Empty_Prog});
|
wneuper@59472
|
488 |
\<close>
|
wneuper@59472
|
489 |
ML\<open>
|
neuper@37954
|
490 |
(* isolate the bound variable in an d2 equation with pqFormula;
|
neuper@37954
|
491 |
'bdv' is a meta-constant*)
|
s1210629013@55444
|
492 |
val d2_polyeq_pqFormula_simplify = prep_rls'(
|
walther@59851
|
493 |
Rule_Def.Repeat {id = "d2_polyeq_pqFormula_simplify", preconds = [],
|
walther@60358
|
494 |
rew_ord = ("e_rew_ord",Rewrite_Ord.e_rew_ord), erls = PolyEq_erls,
|
walther@60358
|
495 |
srls = Rule_Set.Empty, calc = [], errpatts = [],
|
walther@60358
|
496 |
rules = [
|
walther@60358
|
497 |
\<^rule_thm>\<open>d2_pqformula1\<close>, (* q+px+ x^2=0 *)
|
walther@60358
|
498 |
\<^rule_thm>\<open>d2_pqformula1_neg\<close>, (* q+px+ x^2=0 *)
|
walther@60358
|
499 |
\<^rule_thm>\<open>d2_pqformula2\<close>, (* q+px+1x^2=0 *)
|
walther@60358
|
500 |
\<^rule_thm>\<open>d2_pqformula2_neg\<close>, (* q+px+1x^2=0 *)
|
walther@60358
|
501 |
\<^rule_thm>\<open>d2_pqformula3\<close>, (* q+ x+ x^2=0 *)
|
walther@60358
|
502 |
\<^rule_thm>\<open>d2_pqformula3_neg\<close>, (* q+ x+ x^2=0 *)
|
walther@60358
|
503 |
\<^rule_thm>\<open>d2_pqformula4\<close>, (* q+ x+1x^2=0 *)
|
walther@60358
|
504 |
\<^rule_thm>\<open>d2_pqformula4_neg\<close>, (* q+ x+1x^2=0 *)
|
walther@60358
|
505 |
\<^rule_thm>\<open>d2_pqformula5\<close>, (* qx+ x^2=0 *)
|
walther@60358
|
506 |
\<^rule_thm>\<open>d2_pqformula6\<close>, (* qx+1x^2=0 *)
|
walther@60358
|
507 |
\<^rule_thm>\<open>d2_pqformula7\<close>, (* x+ x^2=0 *)
|
walther@60358
|
508 |
\<^rule_thm>\<open>d2_pqformula8\<close>, (* x+1x^2=0 *)
|
walther@60358
|
509 |
\<^rule_thm>\<open>d2_pqformula9\<close>, (* q +1x^2=0 *)
|
walther@60358
|
510 |
\<^rule_thm>\<open>d2_pqformula9_neg\<close>, (* q +1x^2=0 *)
|
walther@60358
|
511 |
\<^rule_thm>\<open>d2_pqformula10\<close>, (* q + x^2=0 *)
|
walther@60358
|
512 |
\<^rule_thm>\<open>d2_pqformula10_neg\<close>, (* q + x^2=0 *)
|
walther@60358
|
513 |
\<^rule_thm>\<open>d2_sqrt_equation2\<close>, (* x^2=0 *)
|
walther@60358
|
514 |
\<^rule_thm>\<open>d2_sqrt_equation3\<close>], (* 1x^2=0 *)
|
walther@60358
|
515 |
scr = Rule.Empty_Prog});
|
walther@60358
|
516 |
|
walther@60358
|
517 |
(* isolate the bound variable in an d2 equation with abcFormula;
|
neuper@37954
|
518 |
'bdv' is a meta-constant*)
|
s1210629013@55444
|
519 |
val d2_polyeq_abcFormula_simplify = prep_rls'(
|
walther@59851
|
520 |
Rule_Def.Repeat {id = "d2_polyeq_abcFormula_simplify", preconds = [],
|
walther@60358
|
521 |
rew_ord = ("e_rew_ord",Rewrite_Ord.e_rew_ord), erls = PolyEq_erls,
|
walther@60358
|
522 |
srls = Rule_Set.Empty, calc = [], errpatts = [],
|
walther@60358
|
523 |
rules = [
|
walther@60358
|
524 |
\<^rule_thm>\<open>d2_abcformula1\<close>, (*c+bx+cx^2=0 *)
|
walther@60358
|
525 |
\<^rule_thm>\<open>d2_abcformula1_neg\<close>, (*c+bx+cx^2=0 *)
|
walther@60358
|
526 |
\<^rule_thm>\<open>d2_abcformula2\<close>, (*c+ x+cx^2=0 *)
|
walther@60358
|
527 |
\<^rule_thm>\<open>d2_abcformula2_neg\<close>, (*c+ x+cx^2=0 *)
|
walther@60358
|
528 |
\<^rule_thm>\<open>d2_abcformula3\<close>, (*c+bx+ x^2=0 *)
|
walther@60358
|
529 |
\<^rule_thm>\<open>d2_abcformula3_neg\<close>, (*c+bx+ x^2=0 *)
|
walther@60358
|
530 |
\<^rule_thm>\<open>d2_abcformula4\<close>, (*c+ x+ x^2=0 *)
|
walther@60358
|
531 |
\<^rule_thm>\<open>d2_abcformula4_neg\<close>, (*c+ x+ x^2=0 *)
|
walther@60358
|
532 |
\<^rule_thm>\<open>d2_abcformula5\<close>, (*c+ cx^2=0 *)
|
walther@60358
|
533 |
\<^rule_thm>\<open>d2_abcformula5_neg\<close>, (*c+ cx^2=0 *)
|
walther@60358
|
534 |
\<^rule_thm>\<open>d2_abcformula6\<close>, (*c+ x^2=0 *)
|
walther@60358
|
535 |
\<^rule_thm>\<open>d2_abcformula6_neg\<close>, (*c+ x^2=0 *)
|
walther@60358
|
536 |
\<^rule_thm>\<open>d2_abcformula7\<close>, (* bx+ax^2=0 *)
|
walther@60358
|
537 |
\<^rule_thm>\<open>d2_abcformula8\<close>, (* bx+ x^2=0 *)
|
walther@60358
|
538 |
\<^rule_thm>\<open>d2_abcformula9\<close>, (* x+ax^2=0 *)
|
walther@60358
|
539 |
\<^rule_thm>\<open>d2_abcformula10\<close>, (* x+ x^2=0 *)
|
walther@60358
|
540 |
\<^rule_thm>\<open>d2_sqrt_equation2\<close>, (* x^2=0 *)
|
walther@60358
|
541 |
\<^rule_thm>\<open>d2_sqrt_equation3\<close>], (* bx^2=0 *)
|
walther@60358
|
542 |
scr = Rule.Empty_Prog});
|
neuper@37954
|
543 |
|
neuper@37954
|
544 |
(* isolate the bound variable in an d2 equation;
|
neuper@37954
|
545 |
'bdv' is a meta-constant*)
|
s1210629013@55444
|
546 |
val d2_polyeq_simplify = prep_rls'(
|
walther@59851
|
547 |
Rule_Def.Repeat {id = "d2_polyeq_simplify", preconds = [],
|
walther@60358
|
548 |
rew_ord = ("e_rew_ord",Rewrite_Ord.e_rew_ord), erls = PolyEq_erls,
|
walther@60358
|
549 |
srls = Rule_Set.Empty, calc = [], errpatts = [],
|
walther@60358
|
550 |
rules = [
|
walther@60358
|
551 |
\<^rule_thm>\<open>d2_pqformula1\<close>, (* p+qx+ x^2=0 *)
|
walther@60358
|
552 |
\<^rule_thm>\<open>d2_pqformula1_neg\<close>, (* p+qx+ x^2=0 *)
|
walther@60358
|
553 |
\<^rule_thm>\<open>d2_pqformula2\<close>, (* p+qx+1x^2=0 *)
|
walther@60358
|
554 |
\<^rule_thm>\<open>d2_pqformula2_neg\<close>, (* p+qx+1x^2=0 *)
|
walther@60358
|
555 |
\<^rule_thm>\<open>d2_pqformula3\<close>, (* p+ x+ x^2=0 *)
|
walther@60358
|
556 |
\<^rule_thm>\<open>d2_pqformula3_neg\<close>, (* p+ x+ x^2=0 *)
|
walther@60358
|
557 |
\<^rule_thm>\<open>d2_pqformula4\<close>, (* p+ x+1x^2=0 *)
|
walther@60358
|
558 |
\<^rule_thm>\<open>d2_pqformula4_neg\<close>, (* p+ x+1x^2=0 *)
|
walther@60358
|
559 |
\<^rule_thm>\<open>d2_abcformula1\<close>, (* c+bx+cx^2=0 *)
|
walther@60358
|
560 |
\<^rule_thm>\<open>d2_abcformula1_neg\<close>, (* c+bx+cx^2=0 *)
|
walther@60358
|
561 |
\<^rule_thm>\<open>d2_abcformula2\<close>, (* c+ x+cx^2=0 *)
|
walther@60358
|
562 |
\<^rule_thm>\<open>d2_abcformula2_neg\<close>, (* c+ x+cx^2=0 *)
|
walther@60358
|
563 |
\<^rule_thm>\<open>d2_prescind1\<close>, (* ax+bx^2=0 -> x(a+bx)=0 *)
|
walther@60358
|
564 |
\<^rule_thm>\<open>d2_prescind2\<close>, (* ax+ x^2=0 -> x(a+ x)=0 *)
|
walther@60358
|
565 |
\<^rule_thm>\<open>d2_prescind3\<close>, (* x+bx^2=0 -> x(1+bx)=0 *)
|
walther@60358
|
566 |
\<^rule_thm>\<open>d2_prescind4\<close>, (* x+ x^2=0 -> x(1+ x)=0 *)
|
walther@60358
|
567 |
\<^rule_thm>\<open>d2_isolate_add1\<close>, (* a+ bx^2=0 -> bx^2=(-1)a*)
|
walther@60358
|
568 |
\<^rule_thm>\<open>d2_isolate_add2\<close>, (* a+ x^2=0 -> x^2=(-1)a*)
|
walther@60358
|
569 |
\<^rule_thm>\<open>d2_sqrt_equation1\<close>, (* x^2=c -> x=+-sqrt(c)*)
|
walther@60358
|
570 |
\<^rule_thm>\<open>d2_sqrt_equation1_neg\<close>, (* [c<0] x^2=c -> x=[]*)
|
walther@60358
|
571 |
\<^rule_thm>\<open>d2_sqrt_equation2\<close>, (* x^2=0 -> x=0 *)
|
walther@60358
|
572 |
\<^rule_thm>\<open>d2_reduce_equation1\<close>, (* x(a+bx)=0 -> x=0 | a+bx=0*)
|
walther@60358
|
573 |
\<^rule_thm>\<open>d2_reduce_equation2\<close>, (* x(a+ x)=0 -> x=0 | a+ x=0*)
|
walther@60358
|
574 |
\<^rule_thm>\<open>d2_isolate_div\<close>], (* bx^2=c -> x^2=c/b*)
|
walther@60358
|
575 |
scr = Rule.Empty_Prog});
|
neuper@37954
|
576 |
|
neuper@37954
|
577 |
(* -- d3 -- *)
|
neuper@37954
|
578 |
(* isolate the bound variable in an d3 equation; 'bdv' is a meta-constant *)
|
s1210629013@55444
|
579 |
val d3_polyeq_simplify = prep_rls'(
|
walther@59851
|
580 |
Rule_Def.Repeat {id = "d3_polyeq_simplify", preconds = [],
|
walther@60358
|
581 |
rew_ord = ("e_rew_ord",Rewrite_Ord.e_rew_ord), erls = PolyEq_erls,
|
walther@60358
|
582 |
srls = Rule_Set.Empty, calc = [], errpatts = [],
|
walther@60358
|
583 |
rules = [
|
walther@60358
|
584 |
\<^rule_thm>\<open>d3_reduce_equation1\<close>, (*a*bdv + b*bdv \<up> 2 + c*bdv \<up> 3=0) = (bdv=0 | (a + b*bdv + c*bdv \<up> 2=0)*)
|
walther@60358
|
585 |
\<^rule_thm>\<open>d3_reduce_equation2\<close>, (* bdv + b*bdv \<up> 2 + c*bdv \<up> 3=0) = (bdv=0 | (1 + b*bdv + c*bdv \<up> 2=0)*)
|
walther@60358
|
586 |
\<^rule_thm>\<open>d3_reduce_equation3\<close>, (*a*bdv + bdv \<up> 2 + c*bdv \<up> 3=0) = (bdv=0 | (a + bdv + c*bdv \<up> 2=0)*)
|
walther@60358
|
587 |
\<^rule_thm>\<open>d3_reduce_equation4\<close>, (* bdv + bdv \<up> 2 + c*bdv \<up> 3=0) = (bdv=0 | (1 + bdv + c*bdv \<up> 2=0)*)
|
walther@60358
|
588 |
\<^rule_thm>\<open>d3_reduce_equation5\<close>, (*a*bdv + b*bdv \<up> 2 + bdv \<up> 3=0) = (bdv=0 | (a + b*bdv + bdv \<up> 2=0)*)
|
walther@60358
|
589 |
\<^rule_thm>\<open>d3_reduce_equation6\<close>, (* bdv + b*bdv \<up> 2 + bdv \<up> 3=0) = (bdv=0 | (1 + b*bdv + bdv \<up> 2=0)*)
|
walther@60358
|
590 |
\<^rule_thm>\<open>d3_reduce_equation7\<close>, (*a*bdv + bdv \<up> 2 + bdv \<up> 3=0) = (bdv=0 | (1 + bdv + bdv \<up> 2=0)*)
|
walther@60358
|
591 |
\<^rule_thm>\<open>d3_reduce_equation8\<close>, (* bdv + bdv \<up> 2 + bdv \<up> 3=0) = (bdv=0 | (1 + bdv + bdv \<up> 2=0)*)
|
walther@60358
|
592 |
\<^rule_thm>\<open>d3_reduce_equation9\<close>, (*a*bdv + c*bdv \<up> 3=0) = (bdv=0 | (a + c*bdv \<up> 2=0)*)
|
walther@60358
|
593 |
\<^rule_thm>\<open>d3_reduce_equation10\<close>, (* bdv + c*bdv \<up> 3=0) = (bdv=0 | (1 + c*bdv \<up> 2=0)*)
|
walther@60358
|
594 |
\<^rule_thm>\<open>d3_reduce_equation11\<close>, (*a*bdv + bdv \<up> 3=0) = (bdv=0 | (a + bdv \<up> 2=0)*)
|
walther@60358
|
595 |
\<^rule_thm>\<open>d3_reduce_equation12\<close>, (* bdv + bdv \<up> 3=0) = (bdv=0 | (1 + bdv \<up> 2=0)*)
|
walther@60358
|
596 |
\<^rule_thm>\<open>d3_reduce_equation13\<close>, (* b*bdv \<up> 2 + c*bdv \<up> 3=0) = (bdv=0 | ( b*bdv + c*bdv \<up> 2=0)*)
|
walther@60358
|
597 |
\<^rule_thm>\<open>d3_reduce_equation14\<close>, (* bdv \<up> 2 + c*bdv \<up> 3=0) = (bdv=0 | ( bdv + c*bdv \<up> 2=0)*)
|
walther@60358
|
598 |
\<^rule_thm>\<open>d3_reduce_equation15\<close>, (* b*bdv \<up> 2 + bdv \<up> 3=0) = (bdv=0 | ( b*bdv + bdv \<up> 2=0)*)
|
walther@60358
|
599 |
\<^rule_thm>\<open>d3_reduce_equation16\<close>, (* bdv \<up> 2 + bdv \<up> 3=0) = (bdv=0 | ( bdv + bdv \<up> 2=0)*)
|
walther@60358
|
600 |
\<^rule_thm>\<open>d3_isolate_add1\<close>, (*[|Not(bdv occurs_in a)|] ==> (a + b*bdv \<up> 3=0) = (bdv=0 | (b*bdv \<up> 3=a)*)
|
walther@60358
|
601 |
\<^rule_thm>\<open>d3_isolate_add2\<close>, (*[|Not(bdv occurs_in a)|] ==> (a + bdv \<up> 3=0) = (bdv=0 | ( bdv \<up> 3=a)*)
|
walther@60358
|
602 |
\<^rule_thm>\<open>d3_isolate_div\<close>, (*[|Not(b=0)|] ==> (b*bdv \<up> 3=c) = (bdv \<up> 3=c/b*)
|
walther@60358
|
603 |
\<^rule_thm>\<open>d3_root_equation2\<close>, (*(bdv \<up> 3=0) = (bdv=0) *)
|
walther@60358
|
604 |
\<^rule_thm>\<open>d3_root_equation1\<close>], (*bdv \<up> 3=c) = (bdv = nroot 3 c*)
|
walther@60358
|
605 |
scr = Rule.Empty_Prog});
|
neuper@37954
|
606 |
|
neuper@37954
|
607 |
(* -- d4 -- *)
|
neuper@37954
|
608 |
(*isolate the bound variable in an d4 equation; 'bdv' is a meta-constant*)
|
s1210629013@55444
|
609 |
val d4_polyeq_simplify = prep_rls'(
|
walther@59851
|
610 |
Rule_Def.Repeat {id = "d4_polyeq_simplify", preconds = [],
|
walther@60358
|
611 |
rew_ord = ("e_rew_ord",Rewrite_Ord.e_rew_ord), erls = PolyEq_erls,
|
walther@60358
|
612 |
srls = Rule_Set.Empty, calc = [], errpatts = [],
|
walther@60358
|
613 |
rules = [
|
walther@60358
|
614 |
\<^rule_thm>\<open>d4_sub_u1\<close> (* ax^4+bx^2+c=0 -> x=+-sqrt(ax^2+bx^+c) *)],
|
walther@60358
|
615 |
scr = Rule.Empty_Prog});
|
wneuper@59472
|
616 |
\<close>
|
wenzelm@60289
|
617 |
rule_set_knowledge
|
wenzelm@60286
|
618 |
d0_polyeq_simplify = d0_polyeq_simplify and
|
wenzelm@60286
|
619 |
d1_polyeq_simplify = d1_polyeq_simplify and
|
wenzelm@60286
|
620 |
d2_polyeq_simplify = d2_polyeq_simplify and
|
wenzelm@60286
|
621 |
d2_polyeq_bdv_only_simplify = d2_polyeq_bdv_only_simplify and
|
wenzelm@60286
|
622 |
d2_polyeq_sq_only_simplify = d2_polyeq_sq_only_simplify and
|
neuper@52125
|
623 |
|
wenzelm@60286
|
624 |
d2_polyeq_pqFormula_simplify = d2_polyeq_pqFormula_simplify and
|
wenzelm@60286
|
625 |
d2_polyeq_abcFormula_simplify = d2_polyeq_abcFormula_simplify and
|
wenzelm@60286
|
626 |
d3_polyeq_simplify = d3_polyeq_simplify and
|
wenzelm@60286
|
627 |
d4_polyeq_simplify = d4_polyeq_simplify
|
walther@60258
|
628 |
|
wenzelm@60306
|
629 |
problem pbl_equ_univ_poly : "polynomial/univariate/equation" =
|
wenzelm@60306
|
630 |
\<open>PolyEq_prls\<close>
|
wenzelm@60306
|
631 |
CAS: "solve (e_e::bool, v_v)"
|
wenzelm@60306
|
632 |
Given: "equality e_e" "solveFor v_v"
|
wenzelm@60306
|
633 |
Where:
|
wenzelm@60306
|
634 |
"~((e_e::bool) is_ratequation_in (v_v::real))"
|
wenzelm@60306
|
635 |
"~((lhs e_e) is_rootTerm_in (v_v::real))"
|
wenzelm@60306
|
636 |
"~((rhs e_e) is_rootTerm_in (v_v::real))"
|
wenzelm@60306
|
637 |
Find: "solutions v_v'i'"
|
wenzelm@60306
|
638 |
|
wenzelm@60306
|
639 |
(*--- d0 ---*)
|
wenzelm@60306
|
640 |
problem pbl_equ_univ_poly_deg0 : "degree_0/polynomial/univariate/equation" =
|
wenzelm@60306
|
641 |
\<open>PolyEq_prls\<close>
|
wenzelm@60306
|
642 |
Method: "PolyEq/solve_d0_polyeq_equation"
|
wenzelm@60306
|
643 |
CAS: "solve (e_e::bool, v_v)"
|
wenzelm@60306
|
644 |
Given: "equality e_e" "solveFor v_v"
|
wenzelm@60306
|
645 |
Where:
|
wenzelm@60306
|
646 |
"matches (?a = 0) e_e"
|
wenzelm@60306
|
647 |
"(lhs e_e) is_poly_in v_v"
|
wenzelm@60306
|
648 |
"((lhs e_e) has_degree_in v_v ) = 0"
|
wenzelm@60306
|
649 |
Find: "solutions v_v'i'"
|
wenzelm@60306
|
650 |
|
wenzelm@60306
|
651 |
(*--- d1 ---*)
|
wenzelm@60306
|
652 |
problem pbl_equ_univ_poly_deg1 : "degree_1/polynomial/univariate/equation" =
|
wenzelm@60306
|
653 |
\<open>PolyEq_prls\<close>
|
wenzelm@60306
|
654 |
Method: "PolyEq/solve_d1_polyeq_equation"
|
wenzelm@60306
|
655 |
CAS: "solve (e_e::bool, v_v)"
|
wenzelm@60306
|
656 |
Given: "equality e_e" "solveFor v_v"
|
wenzelm@60306
|
657 |
Where:
|
wenzelm@60306
|
658 |
"matches (?a = 0) e_e"
|
wenzelm@60306
|
659 |
"(lhs e_e) is_poly_in v_v"
|
wenzelm@60306
|
660 |
"((lhs e_e) has_degree_in v_v ) = 1"
|
wenzelm@60306
|
661 |
Find: "solutions v_v'i'"
|
wenzelm@60306
|
662 |
|
wenzelm@60306
|
663 |
(*--- d2 ---*)
|
wenzelm@60306
|
664 |
problem pbl_equ_univ_poly_deg2 : "degree_2/polynomial/univariate/equation" =
|
wenzelm@60306
|
665 |
\<open>PolyEq_prls\<close>
|
wenzelm@60306
|
666 |
Method: "PolyEq/solve_d2_polyeq_equation"
|
wenzelm@60306
|
667 |
CAS: "solve (e_e::bool, v_v)"
|
wenzelm@60306
|
668 |
Given: "equality e_e" "solveFor v_v"
|
wenzelm@60306
|
669 |
Where:
|
wenzelm@60306
|
670 |
"matches (?a = 0) e_e"
|
wenzelm@60306
|
671 |
"(lhs e_e) is_poly_in v_v "
|
wenzelm@60306
|
672 |
"((lhs e_e) has_degree_in v_v ) = 2"
|
wenzelm@60306
|
673 |
Find: "solutions v_v'i'"
|
wenzelm@60306
|
674 |
|
wenzelm@60306
|
675 |
problem pbl_equ_univ_poly_deg2_sqonly : "sq_only/degree_2/polynomial/univariate/equation" =
|
wenzelm@60306
|
676 |
\<open>PolyEq_prls\<close>
|
wenzelm@60306
|
677 |
Method: "PolyEq/solve_d2_polyeq_sqonly_equation"
|
wenzelm@60306
|
678 |
CAS: "solve (e_e::bool, v_v)"
|
wenzelm@60306
|
679 |
Given: "equality e_e" "solveFor v_v"
|
wenzelm@60306
|
680 |
Where:
|
wenzelm@60306
|
681 |
"matches ( ?a + ?v_ \<up> 2 = 0) e_e |
|
wenzelm@60306
|
682 |
matches ( ?a + ?b*?v_ \<up> 2 = 0) e_e |
|
wenzelm@60306
|
683 |
matches ( ?v_ \<up> 2 = 0) e_e |
|
wenzelm@60306
|
684 |
matches ( ?b*?v_ \<up> 2 = 0) e_e"
|
wenzelm@60306
|
685 |
"Not (matches (?a + ?v_ + ?v_ \<up> 2 = 0) e_e) &
|
wenzelm@60306
|
686 |
Not (matches (?a + ?b*?v_ + ?v_ \<up> 2 = 0) e_e) &
|
wenzelm@60306
|
687 |
Not (matches (?a + ?v_ + ?c*?v_ \<up> 2 = 0) e_e) &
|
wenzelm@60306
|
688 |
Not (matches (?a + ?b*?v_ + ?c*?v_ \<up> 2 = 0) e_e) &
|
wenzelm@60306
|
689 |
Not (matches ( ?v_ + ?v_ \<up> 2 = 0) e_e) &
|
wenzelm@60306
|
690 |
Not (matches ( ?b*?v_ + ?v_ \<up> 2 = 0) e_e) &
|
wenzelm@60306
|
691 |
Not (matches ( ?v_ + ?c*?v_ \<up> 2 = 0) e_e) &
|
wenzelm@60306
|
692 |
Not (matches ( ?b*?v_ + ?c*?v_ \<up> 2 = 0) e_e)"
|
wenzelm@60306
|
693 |
Find: "solutions v_v'i'"
|
wenzelm@60306
|
694 |
|
wenzelm@60306
|
695 |
problem pbl_equ_univ_poly_deg2_bdvonly : "bdv_only/degree_2/polynomial/univariate/equation" =
|
wenzelm@60306
|
696 |
\<open>PolyEq_prls\<close>
|
wenzelm@60306
|
697 |
Method: "PolyEq/solve_d2_polyeq_bdvonly_equation"
|
wenzelm@60306
|
698 |
CAS: "solve (e_e::bool, v_v)"
|
wenzelm@60306
|
699 |
Given: "equality e_e" "solveFor v_v"
|
wenzelm@60306
|
700 |
Where:
|
wenzelm@60306
|
701 |
"matches (?a*?v_ + ?v_ \<up> 2 = 0) e_e |
|
wenzelm@60306
|
702 |
matches ( ?v_ + ?v_ \<up> 2 = 0) e_e |
|
wenzelm@60306
|
703 |
matches ( ?v_ + ?b*?v_ \<up> 2 = 0) e_e |
|
wenzelm@60306
|
704 |
matches (?a*?v_ + ?b*?v_ \<up> 2 = 0) e_e |
|
wenzelm@60306
|
705 |
matches ( ?v_ \<up> 2 = 0) e_e |
|
wenzelm@60306
|
706 |
matches ( ?b*?v_ \<up> 2 = 0) e_e "
|
wenzelm@60306
|
707 |
Find: "solutions v_v'i'"
|
wenzelm@60306
|
708 |
|
wenzelm@60306
|
709 |
problem pbl_equ_univ_poly_deg2_pq : "pqFormula/degree_2/polynomial/univariate/equation" =
|
wenzelm@60306
|
710 |
\<open>PolyEq_prls\<close>
|
wenzelm@60306
|
711 |
Method: "PolyEq/solve_d2_polyeq_pq_equation"
|
wenzelm@60306
|
712 |
CAS: "solve (e_e::bool, v_v)"
|
wenzelm@60306
|
713 |
Given: "equality e_e" "solveFor v_v"
|
wenzelm@60306
|
714 |
Where:
|
wenzelm@60306
|
715 |
"matches (?a + 1*?v_ \<up> 2 = 0) e_e |
|
wenzelm@60306
|
716 |
matches (?a + ?v_ \<up> 2 = 0) e_e"
|
wenzelm@60306
|
717 |
Find: "solutions v_v'i'"
|
wenzelm@60306
|
718 |
|
wenzelm@60306
|
719 |
problem pbl_equ_univ_poly_deg2_abc : "abcFormula/degree_2/polynomial/univariate/equation" =
|
wenzelm@60306
|
720 |
\<open>PolyEq_prls\<close>
|
wenzelm@60306
|
721 |
Method: "PolyEq/solve_d2_polyeq_abc_equation"
|
wenzelm@60306
|
722 |
CAS: "solve (e_e::bool, v_v)"
|
wenzelm@60306
|
723 |
Given: "equality e_e" "solveFor v_v"
|
wenzelm@60306
|
724 |
Where:
|
wenzelm@60306
|
725 |
"matches (?a + ?v_ \<up> 2 = 0) e_e |
|
wenzelm@60306
|
726 |
matches (?a + ?b*?v_ \<up> 2 = 0) e_e"
|
wenzelm@60306
|
727 |
Find: "solutions v_v'i'"
|
wenzelm@60306
|
728 |
|
wenzelm@60306
|
729 |
(*--- d3 ---*)
|
wenzelm@60306
|
730 |
problem pbl_equ_univ_poly_deg3 : "degree_3/polynomial/univariate/equation" =
|
wenzelm@60306
|
731 |
\<open>PolyEq_prls\<close>
|
wenzelm@60306
|
732 |
Method: "PolyEq/solve_d3_polyeq_equation"
|
wenzelm@60306
|
733 |
CAS: "solve (e_e::bool, v_v)"
|
wenzelm@60306
|
734 |
Given: "equality e_e" "solveFor v_v"
|
wenzelm@60306
|
735 |
Where:
|
wenzelm@60306
|
736 |
"matches (?a = 0) e_e"
|
wenzelm@60306
|
737 |
"(lhs e_e) is_poly_in v_v"
|
wenzelm@60306
|
738 |
"((lhs e_e) has_degree_in v_v) = 3"
|
wenzelm@60306
|
739 |
Find: "solutions v_v'i'"
|
wenzelm@60306
|
740 |
|
wenzelm@60306
|
741 |
(*--- d4 ---*)
|
wenzelm@60306
|
742 |
problem pbl_equ_univ_poly_deg4 : "degree_4/polynomial/univariate/equation" =
|
wenzelm@60306
|
743 |
\<open>PolyEq_prls\<close>
|
wenzelm@60306
|
744 |
(*Method: "PolyEq/solve_d4_polyeq_equation"*)
|
wenzelm@60306
|
745 |
CAS: "solve (e_e::bool, v_v)"
|
wenzelm@60306
|
746 |
Given: "equality e_e" "solveFor v_v"
|
wenzelm@60306
|
747 |
Where:
|
wenzelm@60306
|
748 |
"matches (?a = 0) e_e"
|
wenzelm@60306
|
749 |
"(lhs e_e) is_poly_in v_v"
|
wenzelm@60306
|
750 |
"((lhs e_e) has_degree_in v_v) = 4"
|
wenzelm@60306
|
751 |
Find: "solutions v_v'i'"
|
wenzelm@60306
|
752 |
|
wenzelm@60306
|
753 |
(*--- normalise ---*)
|
wenzelm@60306
|
754 |
problem pbl_equ_univ_poly_norm : "normalise/polynomial/univariate/equation" =
|
wenzelm@60306
|
755 |
\<open>PolyEq_prls\<close>
|
wenzelm@60306
|
756 |
Method: "PolyEq/normalise_poly"
|
wenzelm@60306
|
757 |
CAS: "solve (e_e::bool, v_v)"
|
wenzelm@60306
|
758 |
Given: "equality e_e" "solveFor v_v"
|
wenzelm@60306
|
759 |
Where:
|
wenzelm@60306
|
760 |
"(Not((matches (?a = 0 ) e_e ))) |
|
wenzelm@60306
|
761 |
(Not(((lhs e_e) is_poly_in v_v)))"
|
wenzelm@60306
|
762 |
Find: "solutions v_v'i'"
|
wenzelm@60306
|
763 |
|
wenzelm@60306
|
764 |
(*-------------------------expanded-----------------------*)
|
wenzelm@60306
|
765 |
problem "pbl_equ_univ_expand" : "expanded/univariate/equation" =
|
wenzelm@60306
|
766 |
\<open>PolyEq_prls\<close>
|
wenzelm@60306
|
767 |
CAS: "solve (e_e::bool, v_v)"
|
wenzelm@60306
|
768 |
Given: "equality e_e" "solveFor v_v"
|
wenzelm@60306
|
769 |
Where:
|
wenzelm@60306
|
770 |
"matches (?a = 0) e_e"
|
wenzelm@60306
|
771 |
"(lhs e_e) is_expanded_in v_v "
|
wenzelm@60306
|
772 |
Find: "solutions v_v'i'"
|
wenzelm@60306
|
773 |
|
wenzelm@60306
|
774 |
(*--- d2 ---*)
|
wenzelm@60306
|
775 |
problem pbl_equ_univ_expand_deg2 : "degree_2/expanded/univariate/equation" =
|
wenzelm@60306
|
776 |
\<open>PolyEq_prls\<close>
|
wenzelm@60306
|
777 |
Method: "PolyEq/complete_square"
|
wenzelm@60306
|
778 |
CAS: "solve (e_e::bool, v_v)"
|
wenzelm@60306
|
779 |
Given: "equality e_e" "solveFor v_v"
|
wenzelm@60306
|
780 |
Where: "((lhs e_e) has_degree_in v_v) = 2"
|
wenzelm@60306
|
781 |
Find: "solutions v_v'i'"
|
neuper@37954
|
782 |
|
wneuper@59472
|
783 |
text \<open>"-------------------------methods-----------------------"\<close>
|
wenzelm@60303
|
784 |
|
wenzelm@60303
|
785 |
method met_polyeq : "PolyEq" =
|
wenzelm@60303
|
786 |
\<open>{rew_ord'="tless_true",rls'=Atools_erls,calc = [], srls = Rule_Set.empty, prls=Rule_Set.empty,
|
wenzelm@60303
|
787 |
crls=PolyEq_crls, errpats = [], nrls = norm_Rational}\<close>
|
wneuper@59545
|
788 |
|
wneuper@59504
|
789 |
partial_function (tailrec) normalize_poly_eq :: "bool \<Rightarrow> real \<Rightarrow> bool"
|
wneuper@59504
|
790 |
where
|
walther@59635
|
791 |
"normalize_poly_eq e_e v_v = (
|
walther@59635
|
792 |
let
|
walther@59635
|
793 |
e_e = (
|
walther@59637
|
794 |
(Try (Rewrite ''all_left'')) #>
|
walther@59637
|
795 |
(Try (Repeat (Rewrite ''makex1_x''))) #>
|
walther@59637
|
796 |
(Try (Repeat (Rewrite_Set ''expand_binoms''))) #>
|
walther@59637
|
797 |
(Try (Repeat (Rewrite_Set_Inst [(''bdv'', v_v)] ''make_ratpoly_in''))) #>
|
walther@59635
|
798 |
(Try (Repeat (Rewrite_Set ''polyeq_simplify''))) ) e_e
|
walther@59635
|
799 |
in
|
walther@59635
|
800 |
SubProblem (''PolyEq'', [''polynomial'', ''univariate'', ''equation''], [''no_met''])
|
wneuper@59504
|
801 |
[BOOL e_e, REAL v_v])"
|
wenzelm@60303
|
802 |
|
wenzelm@60303
|
803 |
method met_polyeq_norm : "PolyEq/normalise_poly" =
|
wenzelm@60303
|
804 |
\<open>{rew_ord'="termlessI", rls'=PolyEq_erls, srls=Rule_Set.empty, prls=PolyEq_prls, calc=[],
|
wenzelm@60303
|
805 |
crls=PolyEq_crls, errpats = [], nrls = norm_Rational}\<close>
|
wenzelm@60303
|
806 |
Program: normalize_poly_eq.simps
|
wenzelm@60303
|
807 |
Given: "equality e_e" "solveFor v_v"
|
wenzelm@60303
|
808 |
Where: "(Not((matches (?a = 0 ) e_e ))) | (Not(((lhs e_e) is_poly_in v_v)))"
|
wenzelm@60303
|
809 |
Find: "solutions v_v'i'"
|
wneuper@59545
|
810 |
|
wneuper@59504
|
811 |
partial_function (tailrec) solve_poly_equ :: "bool \<Rightarrow> real \<Rightarrow> bool list"
|
wneuper@59504
|
812 |
where
|
walther@59635
|
813 |
"solve_poly_equ e_e v_v = (
|
walther@59635
|
814 |
let
|
walther@59635
|
815 |
e_e = (Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''d0_polyeq_simplify'')) e_e
|
walther@59635
|
816 |
in
|
walther@59635
|
817 |
Or_to_List e_e)"
|
wenzelm@60303
|
818 |
|
wenzelm@60303
|
819 |
method met_polyeq_d0 : "PolyEq/solve_d0_polyeq_equation" =
|
wenzelm@60303
|
820 |
\<open>{rew_ord'="termlessI", rls'=PolyEq_erls, srls=Rule_Set.empty, prls=PolyEq_prls,
|
wenzelm@60309
|
821 |
calc=[("sqrt", (\<^const_name>\<open>sqrt\<close>, eval_sqrt "#sqrt_"))], crls=PolyEq_crls, errpats = [],
|
wenzelm@60303
|
822 |
nrls = norm_Rational}\<close>
|
wenzelm@60303
|
823 |
Program: solve_poly_equ.simps
|
wenzelm@60303
|
824 |
Given: "equality e_e" "solveFor v_v"
|
wenzelm@60303
|
825 |
Where: "(lhs e_e) is_poly_in v_v " "((lhs e_e) has_degree_in v_v) = 0"
|
wenzelm@60303
|
826 |
Find: "solutions v_v'i'"
|
wneuper@59545
|
827 |
|
wneuper@59504
|
828 |
partial_function (tailrec) solve_poly_eq1 :: "bool \<Rightarrow> real \<Rightarrow> bool list"
|
walther@59635
|
829 |
where
|
walther@59635
|
830 |
"solve_poly_eq1 e_e v_v = (
|
walther@59635
|
831 |
let
|
walther@59635
|
832 |
e_e = (
|
walther@59637
|
833 |
(Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''d1_polyeq_simplify'')) #>
|
walther@59637
|
834 |
(Try (Rewrite_Set ''polyeq_simplify'')) #>
|
walther@59635
|
835 |
(Try (Rewrite_Set ''norm_Rational_parenthesized'')) ) e_e;
|
walther@59635
|
836 |
L_L = Or_to_List e_e
|
walther@59635
|
837 |
in
|
walther@59635
|
838 |
Check_elementwise L_L {(v_v::real). Assumptions})"
|
wenzelm@60303
|
839 |
|
wenzelm@60303
|
840 |
method met_polyeq_d1 : "PolyEq/solve_d1_polyeq_equation" =
|
wenzelm@60303
|
841 |
\<open>{rew_ord'="termlessI", rls'=PolyEq_erls, srls=Rule_Set.empty, prls=PolyEq_prls,
|
wenzelm@60309
|
842 |
calc=[("sqrt", (\<^const_name>\<open>sqrt\<close>, eval_sqrt "#sqrt_"))], crls=PolyEq_crls, errpats = [],
|
wenzelm@60303
|
843 |
nrls = norm_Rational}\<close>
|
wenzelm@60303
|
844 |
Program: solve_poly_eq1.simps
|
wenzelm@60303
|
845 |
Given: "equality e_e" "solveFor v_v"
|
wenzelm@60303
|
846 |
Where: "(lhs e_e) is_poly_in v_v" "((lhs e_e) has_degree_in v_v) = 1"
|
wenzelm@60303
|
847 |
Find: "solutions v_v'i'"
|
wneuper@59545
|
848 |
|
wneuper@59504
|
849 |
partial_function (tailrec) solve_poly_equ2 :: "bool \<Rightarrow> real \<Rightarrow> bool list"
|
wneuper@59504
|
850 |
where
|
walther@59635
|
851 |
"solve_poly_equ2 e_e v_v = (
|
walther@59635
|
852 |
let
|
walther@59635
|
853 |
e_e = (
|
walther@59637
|
854 |
(Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''d2_polyeq_simplify'')) #>
|
walther@59637
|
855 |
(Try (Rewrite_Set ''polyeq_simplify'')) #>
|
walther@59637
|
856 |
(Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''d1_polyeq_simplify'')) #>
|
walther@59637
|
857 |
(Try (Rewrite_Set ''polyeq_simplify'')) #>
|
walther@59635
|
858 |
(Try (Rewrite_Set ''norm_Rational_parenthesized'')) ) e_e;
|
walther@59635
|
859 |
L_L = Or_to_List e_e
|
walther@59635
|
860 |
in
|
walther@59635
|
861 |
Check_elementwise L_L {(v_v::real). Assumptions})"
|
wenzelm@60303
|
862 |
|
wenzelm@60303
|
863 |
method met_polyeq_d22 : "PolyEq/solve_d2_polyeq_equation" =
|
wenzelm@60303
|
864 |
\<open>{rew_ord'="termlessI", rls'=PolyEq_erls, srls=Rule_Set.empty, prls=PolyEq_prls,
|
wenzelm@60309
|
865 |
calc=[("sqrt", (\<^const_name>\<open>sqrt\<close>, eval_sqrt "#sqrt_"))], crls=PolyEq_crls, errpats = [],
|
wenzelm@60303
|
866 |
nrls = norm_Rational}\<close>
|
wenzelm@60303
|
867 |
Program: solve_poly_equ2.simps
|
wenzelm@60303
|
868 |
Given: "equality e_e" "solveFor v_v"
|
wenzelm@60303
|
869 |
Where: "(lhs e_e) is_poly_in v_v " "((lhs e_e) has_degree_in v_v) = 2"
|
wenzelm@60303
|
870 |
Find: "solutions v_v'i'"
|
wneuper@59545
|
871 |
|
wneuper@59504
|
872 |
partial_function (tailrec) solve_poly_equ0 :: "bool \<Rightarrow> real \<Rightarrow> bool list"
|
walther@59635
|
873 |
where
|
walther@59635
|
874 |
"solve_poly_equ0 e_e v_v = (
|
walther@59635
|
875 |
let
|
walther@59635
|
876 |
e_e = (
|
walther@59637
|
877 |
(Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''d2_polyeq_bdv_only_simplify'')) #>
|
walther@59637
|
878 |
(Try (Rewrite_Set ''polyeq_simplify'')) #>
|
walther@59637
|
879 |
(Try (Rewrite_Set_Inst [(''bdv'',v_v::real)] ''d1_polyeq_simplify'')) #>
|
walther@59637
|
880 |
(Try (Rewrite_Set ''polyeq_simplify'')) #>
|
walther@59635
|
881 |
(Try (Rewrite_Set ''norm_Rational_parenthesized'')) ) e_e;
|
wneuper@59504
|
882 |
L_L = Or_to_List e_e
|
walther@59635
|
883 |
in
|
walther@59635
|
884 |
Check_elementwise L_L {(v_v::real). Assumptions})"
|
wenzelm@60303
|
885 |
|
wenzelm@60303
|
886 |
method met_polyeq_d2_bdvonly : "PolyEq/solve_d2_polyeq_bdvonly_equation" =
|
wenzelm@60303
|
887 |
\<open>{rew_ord'="termlessI", rls'=PolyEq_erls, srls=Rule_Set.empty, prls=PolyEq_prls,
|
wenzelm@60309
|
888 |
calc=[("sqrt", (\<^const_name>\<open>sqrt\<close>, eval_sqrt "#sqrt_"))], crls=PolyEq_crls, errpats = [],
|
wenzelm@60303
|
889 |
nrls = norm_Rational}\<close>
|
wenzelm@60303
|
890 |
Program: solve_poly_equ0.simps
|
wenzelm@60303
|
891 |
Given: "equality e_e" "solveFor v_v"
|
wenzelm@60303
|
892 |
Where: "(lhs e_e) is_poly_in v_v " "((lhs e_e) has_degree_in v_v) = 2"
|
wenzelm@60303
|
893 |
Find: "solutions v_v'i'"
|
wneuper@59545
|
894 |
|
wneuper@59504
|
895 |
partial_function (tailrec) solve_poly_equ_sqrt :: "bool \<Rightarrow> real \<Rightarrow> bool list"
|
wneuper@59504
|
896 |
where
|
walther@59635
|
897 |
"solve_poly_equ_sqrt e_e v_v = (
|
walther@59635
|
898 |
let
|
walther@59635
|
899 |
e_e = (
|
walther@59637
|
900 |
(Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''d2_polyeq_sq_only_simplify'')) #>
|
walther@59637
|
901 |
(Try (Rewrite_Set ''polyeq_simplify'')) #>
|
walther@59635
|
902 |
(Try (Rewrite_Set ''norm_Rational_parenthesized'')) ) e_e;
|
wneuper@59504
|
903 |
L_L = Or_to_List e_e
|
walther@59635
|
904 |
in
|
walther@59635
|
905 |
Check_elementwise L_L {(v_v::real). Assumptions})"
|
wenzelm@60303
|
906 |
|
wenzelm@60303
|
907 |
method met_polyeq_d2_sqonly : "PolyEq/solve_d2_polyeq_sqonly_equation" =
|
wenzelm@60303
|
908 |
\<open>{rew_ord'="termlessI", rls'=PolyEq_erls, srls=Rule_Set.empty, prls=PolyEq_prls,
|
wenzelm@60309
|
909 |
calc=[("sqrt", (\<^const_name>\<open>sqrt\<close>, eval_sqrt "#sqrt_"))], crls=PolyEq_crls, errpats = [],
|
wenzelm@60303
|
910 |
nrls = norm_Rational}\<close>
|
wenzelm@60303
|
911 |
Program: solve_poly_equ_sqrt.simps
|
wenzelm@60303
|
912 |
Given: "equality e_e" "solveFor v_v"
|
wenzelm@60303
|
913 |
Where: "(lhs e_e) is_poly_in v_v " "((lhs e_e) has_degree_in v_v) = 2"
|
wenzelm@60303
|
914 |
Find: "solutions v_v'i'"
|
wneuper@59545
|
915 |
|
wneuper@59504
|
916 |
partial_function (tailrec) solve_poly_equ_pq :: "bool \<Rightarrow> real \<Rightarrow> bool list"
|
walther@59635
|
917 |
where
|
walther@59635
|
918 |
"solve_poly_equ_pq e_e v_v = (
|
walther@59635
|
919 |
let
|
walther@59635
|
920 |
e_e = (
|
walther@59637
|
921 |
(Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''d2_polyeq_pqFormula_simplify'')) #>
|
walther@59637
|
922 |
(Try (Rewrite_Set ''polyeq_simplify'')) #>
|
walther@59635
|
923 |
(Try (Rewrite_Set ''norm_Rational_parenthesized'')) ) e_e;
|
walther@59635
|
924 |
L_L = Or_to_List e_e
|
walther@59635
|
925 |
in
|
walther@59635
|
926 |
Check_elementwise L_L {(v_v::real). Assumptions})"
|
wenzelm@60303
|
927 |
|
wenzelm@60303
|
928 |
method met_polyeq_d2_pq : "PolyEq/solve_d2_polyeq_pq_equation" =
|
wenzelm@60303
|
929 |
\<open>{rew_ord'="termlessI", rls'=PolyEq_erls, srls=Rule_Set.empty, prls=PolyEq_prls,
|
wenzelm@60309
|
930 |
calc=[("sqrt", (\<^const_name>\<open>sqrt\<close>, eval_sqrt "#sqrt_"))], crls=PolyEq_crls, errpats = [],
|
wenzelm@60303
|
931 |
nrls = norm_Rational}\<close>
|
wenzelm@60303
|
932 |
Program: solve_poly_equ_pq.simps
|
wenzelm@60303
|
933 |
Given: "equality e_e" "solveFor v_v"
|
wenzelm@60303
|
934 |
Where: "(lhs e_e) is_poly_in v_v " "((lhs e_e) has_degree_in v_v) = 2"
|
wenzelm@60303
|
935 |
Find: "solutions v_v'i'"
|
wneuper@59545
|
936 |
|
wneuper@59504
|
937 |
partial_function (tailrec) solve_poly_equ_abc :: "bool \<Rightarrow> real \<Rightarrow> bool list"
|
wneuper@59504
|
938 |
where
|
walther@59635
|
939 |
"solve_poly_equ_abc e_e v_v = (
|
walther@59635
|
940 |
let
|
walther@59635
|
941 |
e_e = (
|
walther@59637
|
942 |
(Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''d2_polyeq_abcFormula_simplify'')) #>
|
walther@59637
|
943 |
(Try (Rewrite_Set ''polyeq_simplify'')) #>
|
walther@59635
|
944 |
(Try (Rewrite_Set ''norm_Rational_parenthesized'')) ) e_e;
|
walther@59635
|
945 |
L_L = Or_to_List e_e
|
wneuper@59504
|
946 |
in Check_elementwise L_L {(v_v::real). Assumptions})"
|
wenzelm@60303
|
947 |
|
wenzelm@60303
|
948 |
method met_polyeq_d2_abc : "PolyEq/solve_d2_polyeq_abc_equation" =
|
wenzelm@60303
|
949 |
\<open>{rew_ord'="termlessI", rls'=PolyEq_erls,srls=Rule_Set.empty, prls=PolyEq_prls,
|
wenzelm@60309
|
950 |
calc=[("sqrt", (\<^const_name>\<open>sqrt\<close>, eval_sqrt "#sqrt_"))], crls=PolyEq_crls, errpats = [],
|
wenzelm@60303
|
951 |
nrls = norm_Rational}\<close>
|
wenzelm@60303
|
952 |
Program: solve_poly_equ_abc.simps
|
wenzelm@60303
|
953 |
Given: "equality e_e" "solveFor v_v"
|
wenzelm@60303
|
954 |
Where: "(lhs e_e) is_poly_in v_v " "((lhs e_e) has_degree_in v_v) = 2"
|
wenzelm@60303
|
955 |
Find: "solutions v_v'i'"
|
wneuper@59545
|
956 |
|
wneuper@59504
|
957 |
partial_function (tailrec) solve_poly_equ3 :: "bool \<Rightarrow> real \<Rightarrow> bool list"
|
walther@59635
|
958 |
where
|
walther@59635
|
959 |
"solve_poly_equ3 e_e v_v = (
|
walther@59635
|
960 |
let
|
walther@59635
|
961 |
e_e = (
|
walther@59637
|
962 |
(Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''d3_polyeq_simplify'')) #>
|
walther@59637
|
963 |
(Try (Rewrite_Set ''polyeq_simplify'')) #>
|
walther@59637
|
964 |
(Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''d2_polyeq_simplify'')) #>
|
walther@59637
|
965 |
(Try (Rewrite_Set ''polyeq_simplify'')) #>
|
walther@59637
|
966 |
(Try (Rewrite_Set_Inst [(''bdv'',v_v)] ''d1_polyeq_simplify'')) #>
|
walther@59637
|
967 |
(Try (Rewrite_Set ''polyeq_simplify'')) #>
|
walther@59635
|
968 |
(Try (Rewrite_Set ''norm_Rational_parenthesized''))) e_e;
|
walther@59635
|
969 |
L_L = Or_to_List e_e
|
walther@59635
|
970 |
in
|
walther@59635
|
971 |
Check_elementwise L_L {(v_v::real). Assumptions})"
|
wenzelm@60303
|
972 |
|
wenzelm@60303
|
973 |
method met_polyeq_d3 : "PolyEq/solve_d3_polyeq_equation" =
|
wenzelm@60303
|
974 |
\<open>{rew_ord'="termlessI", rls'=PolyEq_erls, srls=Rule_Set.empty, prls=PolyEq_prls,
|
wenzelm@60309
|
975 |
calc=[("sqrt", (\<^const_name>\<open>sqrt\<close>, eval_sqrt "#sqrt_"))], crls=PolyEq_crls, errpats = [],
|
wenzelm@60303
|
976 |
nrls = norm_Rational}\<close>
|
wenzelm@60303
|
977 |
Program: solve_poly_equ3.simps
|
wenzelm@60303
|
978 |
Given: "equality e_e" "solveFor v_v"
|
wenzelm@60303
|
979 |
Where: "(lhs e_e) is_poly_in v_v " "((lhs e_e) has_degree_in v_v) = 3"
|
wenzelm@60303
|
980 |
Find: "solutions v_v'i'"
|
wenzelm@60303
|
981 |
|
wenzelm@60303
|
982 |
(*.solves all expanded (ie. normalised) terms of degree 2.*)
|
s1210629013@55373
|
983 |
(*Oct.02 restriction: 'eval_true 0 =< discriminant' ony for integer values
|
s1210629013@55373
|
984 |
by 'PolyEq_erls'; restricted until Float.thy is implemented*)
|
wneuper@59504
|
985 |
partial_function (tailrec) solve_by_completing_square :: "bool \<Rightarrow> real \<Rightarrow> bool list"
|
wneuper@59504
|
986 |
where
|
walther@59635
|
987 |
"solve_by_completing_square e_e v_v = (
|
walther@59635
|
988 |
let e_e = (
|
walther@59637
|
989 |
(Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''cancel_leading_coeff'')) #>
|
walther@59637
|
990 |
(Try (Rewrite_Set_Inst [(''bdv'', v_v)] ''complete_square'')) #>
|
walther@59637
|
991 |
(Try (Rewrite ''square_explicit1'')) #>
|
walther@59637
|
992 |
(Try (Rewrite ''square_explicit2'')) #>
|
walther@59637
|
993 |
(Rewrite ''root_plus_minus'') #>
|
walther@59637
|
994 |
(Try (Repeat (Rewrite_Inst [(''bdv'', v_v)] ''bdv_explicit1''))) #>
|
walther@59637
|
995 |
(Try (Repeat (Rewrite_Inst [(''bdv'', v_v)] ''bdv_explicit2''))) #>
|
walther@59637
|
996 |
(Try (Repeat (Rewrite_Inst [(''bdv'', v_v)] ''bdv_explicit3''))) #>
|
walther@59637
|
997 |
(Try (Rewrite_Set ''calculate_RootRat'')) #>
|
walther@59635
|
998 |
(Try (Repeat (Calculate ''SQRT'')))) e_e
|
walther@59635
|
999 |
in
|
walther@59635
|
1000 |
Or_to_List e_e)"
|
wenzelm@60303
|
1001 |
|
wenzelm@60303
|
1002 |
method met_polyeq_complsq : "PolyEq/complete_square" =
|
wenzelm@60303
|
1003 |
\<open>{rew_ord'="termlessI",rls'=PolyEq_erls,srls=Rule_Set.empty,prls=PolyEq_prls,
|
wenzelm@60309
|
1004 |
calc=[("sqrt", (\<^const_name>\<open>sqrt\<close>, eval_sqrt "#sqrt_"))], crls=PolyEq_crls, errpats = [],
|
wenzelm@60303
|
1005 |
nrls = norm_Rational}\<close>
|
wenzelm@60303
|
1006 |
Program: solve_by_completing_square.simps
|
wenzelm@60303
|
1007 |
Given: "equality e_e" "solveFor v_v"
|
wenzelm@60303
|
1008 |
Where: "matches (?a = 0) e_e" "((lhs e_e) has_degree_in v_v) = 2"
|
wenzelm@60303
|
1009 |
Find: "solutions v_v'i'"
|
s1210629013@55373
|
1010 |
|
wneuper@59472
|
1011 |
ML\<open>
|
neuper@37954
|
1012 |
|
walther@60342
|
1013 |
(* termorder hacked by MG, adapted later by WN *)
|
walther@60342
|
1014 |
(**)local (*. for make_polynomial_in .*)
|
neuper@37954
|
1015 |
|
neuper@37954
|
1016 |
open Term; (* for type order = EQUAL | LESS | GREATER *)
|
neuper@37954
|
1017 |
|
neuper@37954
|
1018 |
fun pr_ord EQUAL = "EQUAL"
|
neuper@37954
|
1019 |
| pr_ord LESS = "LESS"
|
neuper@37954
|
1020 |
| pr_ord GREATER = "GREATER";
|
neuper@37954
|
1021 |
|
walther@60263
|
1022 |
fun dest_hd' _ (Const (a, T)) = (((a, 0), T), 0)
|
walther@60278
|
1023 |
| dest_hd' x (t as Free (a, T)) =
|
neuper@37954
|
1024 |
if x = t then ((("|||||||||||||", 0), T), 0) (*WN*)
|
neuper@37954
|
1025 |
else (((a, 0), T), 1)
|
walther@60263
|
1026 |
| dest_hd' _ (Var v) = (v, 2)
|
walther@60263
|
1027 |
| dest_hd' _ (Bound i) = ((("", i), dummyT), 3)
|
walther@60263
|
1028 |
| dest_hd' _ (Abs (_, T, _)) = ((("", 0), T), 4)
|
walther@60263
|
1029 |
| dest_hd' _ _ = raise ERROR "dest_hd': uncovered case in fun.def.";
|
neuper@37954
|
1030 |
|
wenzelm@60405
|
1031 |
fun size_of_term' i pr x (t as Const (\<^const_name>\<open>realpow\<close>, _) $
|
walther@60342
|
1032 |
Free (var, _) $ Free (pot, _)) =
|
wenzelm@60405
|
1033 |
(if pr then tracing (idt "#" i ^ "size_of_term' realpow: " ^ UnparseC.term t) else ();
|
walther@60342
|
1034 |
case x of (*WN*)
|
walther@60317
|
1035 |
(Free (xstr, _)) =>
|
walther@60342
|
1036 |
if xstr = var
|
walther@60342
|
1037 |
then (if pr then tracing (idt "#" i ^ "xstr = var --> " ^ string_of_int (1000 * (the (TermC.int_opt_of_string pot)))) else ();
|
walther@60342
|
1038 |
1000 * (the (TermC.int_opt_of_string pot)))
|
walther@60342
|
1039 |
else (if pr then tracing (idt "#" i ^ "x <> Free --> " ^ "3") else (); 3)
|
walther@60317
|
1040 |
| _ => raise ERROR ("size_of_term' called with subst = " ^ UnparseC.term x))
|
walther@60342
|
1041 |
| size_of_term' i pr x (t as Abs (_, _, body)) =
|
walther@60342
|
1042 |
(if pr then tracing (idt "#" i ^ "size_of_term' Abs: " ^ UnparseC.term t) else ();
|
walther@60342
|
1043 |
1 + size_of_term' (i + 1) pr x body)
|
walther@60342
|
1044 |
| size_of_term' i pr x (f $ t) =
|
walther@60342
|
1045 |
let
|
walther@60342
|
1046 |
val _ = if pr then tracing (idt "#" i ^ "size_of_term' $$$: " ^ UnparseC.term f ^ " $$$ " ^ UnparseC.term t) else ();
|
walther@60342
|
1047 |
val s1 = size_of_term' (i + 1) pr x f
|
walther@60342
|
1048 |
val s2 = size_of_term' (i + 1) pr x t
|
walther@60342
|
1049 |
val _ = if pr then tracing (idt "#" i ^ "size_of_term' $$$-->: " ^ string_of_int s1 ^ " + " ^ string_of_int s2 ^ " = " ^ string_of_int(s1 + s2)) else ();
|
walther@60342
|
1050 |
in (s1 + s2) end
|
walther@60342
|
1051 |
| size_of_term' i pr x t =
|
walther@60342
|
1052 |
(if pr then tracing (idt "#" i ^ "size_of_term' bot: " ^ UnparseC.term t) else ();
|
walther@60342
|
1053 |
case t of
|
walther@60342
|
1054 |
Free (subst, _) =>
|
walther@60342
|
1055 |
(case x of
|
walther@60342
|
1056 |
Free (xstr, _) =>
|
walther@60342
|
1057 |
if xstr = subst
|
walther@60342
|
1058 |
then (if pr then tracing (idt "#" i ^ "xstr = var --> " ^ "1000") else (); 1000)
|
walther@60342
|
1059 |
else (if pr then tracing (idt "#" i ^ "x <> Free --> " ^ "1") else (); 1)
|
walther@60342
|
1060 |
| _ => raise ERROR ("size_of_term' called with subst = " ^ UnparseC.term x))
|
walther@60342
|
1061 |
| _ => (if pr then tracing (idt "#" i ^ "bot --> " ^ "1") else (); 1));
|
neuper@37954
|
1062 |
|
walther@60342
|
1063 |
fun term_ord' i pr x thy (Abs (_, T, t), Abs(_, U, u)) = (* ~ term.ML *)
|
walther@60342
|
1064 |
let
|
walther@60342
|
1065 |
val _ = if pr then tracing (idt "#" i ^ "term_ord' Abs") else ();
|
walther@60342
|
1066 |
val ord =
|
walther@60342
|
1067 |
case term_ord' (i + 1) pr x thy (t, u) of EQUAL => Term_Ord.typ_ord (T, U) | ord => ord
|
walther@60342
|
1068 |
val _ = if pr then tracing (idt "#" i ^ "term_ord' Abs --> " ^ pr_ord ord) else ()
|
walther@60342
|
1069 |
in ord end
|
walther@60342
|
1070 |
| term_ord' i pr x _ (t, u) =
|
walther@60342
|
1071 |
let
|
walther@60342
|
1072 |
val _ = if pr then tracing (idt "#" i ^ "term_ord' bot (" ^ UnparseC.term t ^ ", " ^ UnparseC.term u ^ ")") else ();
|
walther@60342
|
1073 |
val ord =
|
walther@60342
|
1074 |
case int_ord (size_of_term' (i + 1) pr x t, size_of_term' (i + 1) pr x u) of
|
walther@60342
|
1075 |
EQUAL =>
|
walther@60342
|
1076 |
let val (f, ts) = strip_comb t and (g, us) = strip_comb u
|
walther@60342
|
1077 |
in
|
walther@60342
|
1078 |
(case hd_ord (i + 1) pr x (f, g) of
|
walther@60342
|
1079 |
EQUAL => (terms_ord x (i + 1) pr) (ts, us)
|
walther@60342
|
1080 |
| ord => ord)
|
walther@60342
|
1081 |
end
|
walther@60342
|
1082 |
| ord => ord
|
walther@60342
|
1083 |
val _ = if pr then tracing (idt "#" i ^ "term_ord' bot --> " ^ pr_ord ord) else ()
|
walther@60342
|
1084 |
in ord end
|
walther@60342
|
1085 |
and hd_ord i pr x (f, g) = (* ~ term.ML *)
|
walther@60342
|
1086 |
let
|
walther@60342
|
1087 |
val _ = if pr then tracing (idt "#" i ^ "hd_ord (" ^ UnparseC.term f ^ ", " ^ UnparseC.term g ^ ")") else ();
|
walther@60342
|
1088 |
val ord = prod_ord
|
walther@60342
|
1089 |
(prod_ord Term_Ord.indexname_ord Term_Ord.typ_ord) int_ord
|
walther@60342
|
1090 |
(dest_hd' x f, dest_hd' x g)
|
walther@60342
|
1091 |
val _ = if pr then tracing (idt "#" i ^ "hd_ord --> " ^ pr_ord ord) else ();
|
walther@60342
|
1092 |
in ord end
|
walther@60342
|
1093 |
and terms_ord x i pr (ts, us) =
|
walther@60342
|
1094 |
let
|
walther@60342
|
1095 |
val _ = if pr then tracing (idt "#" i ^ "terms_ord (" ^ UnparseC.terms ts ^ ", " ^ UnparseC.terms us ^ ")") else ();
|
walther@60342
|
1096 |
val ord = list_ord (term_ord' (i + 1) pr x (ThyC.get_theory "Isac_Knowledge"))(ts, us);
|
walther@60342
|
1097 |
val _ = if pr then tracing (idt "#" i ^ "terms_ord --> " ^ pr_ord ord) else ();
|
walther@60342
|
1098 |
in ord end
|
neuper@52070
|
1099 |
|
walther@60342
|
1100 |
(**)in(*local*)
|
neuper@37954
|
1101 |
|
walther@60324
|
1102 |
fun ord_make_polynomial_in (pr:bool) thy subst (ts, us) =
|
walther@60342
|
1103 |
((** )tracing ("*** subs variable is: " ^ Env.subst2str subst); ( **)
|
neuper@37954
|
1104 |
case subst of
|
walther@60342
|
1105 |
(_, x) :: _ =>
|
walther@60342
|
1106 |
term_ord' 1 pr x thy (TermC.numerals_to_Free ts, TermC.numerals_to_Free us) = LESS
|
walther@60263
|
1107 |
| _ => raise ERROR ("ord_make_polynomial_in called with subst = " ^ Env.subst2str subst))
|
walther@60263
|
1108 |
|
neuper@37989
|
1109 |
end;(*local*)
|
neuper@37954
|
1110 |
|
wneuper@59472
|
1111 |
\<close>
|
wneuper@59472
|
1112 |
ML\<open>
|
s1210629013@55444
|
1113 |
val order_add_mult_in = prep_rls'(
|
walther@59851
|
1114 |
Rule_Def.Repeat{id = "order_add_mult_in", preconds = [],
|
walther@60358
|
1115 |
rew_ord = ("ord_make_polynomial_in", ord_make_polynomial_in false @{theory "Poly"}),
|
walther@60358
|
1116 |
erls = Rule_Set.empty,srls = Rule_Set.Empty,
|
walther@60358
|
1117 |
calc = [], errpatts = [],
|
walther@60358
|
1118 |
rules = [
|
walther@60358
|
1119 |
\<^rule_thm>\<open>mult.commute\<close>, (* z * w = w * z *)
|
walther@60358
|
1120 |
\<^rule_thm>\<open>real_mult_left_commute\<close>, (*z1.0 * (z2.0 * z3.0) = z2.0 * (z1.0 * z3.0)*)
|
walther@60358
|
1121 |
\<^rule_thm>\<open>mult.assoc\<close>, (*z1.0 * z2.0 * z3.0 = z1.0 * (z2.0 * z3.0)*)
|
walther@60358
|
1122 |
\<^rule_thm>\<open>add.commute\<close>, (*z + w = w + z*)
|
walther@60358
|
1123 |
\<^rule_thm>\<open>add.left_commute\<close>, (*x + (y + z) = y + (x + z)*)
|
walther@60358
|
1124 |
\<^rule_thm>\<open>add.assoc\<close>], (*z1.0 + z2.0 + z3.0 = z1.0 + (z2.0 + z3.0)*)
|
walther@60358
|
1125 |
scr = Rule.Empty_Prog});
|
neuper@37954
|
1126 |
|
wneuper@59472
|
1127 |
\<close>
|
wneuper@59472
|
1128 |
ML\<open>
|
s1210629013@55444
|
1129 |
val collect_bdv = prep_rls'(
|
walther@59851
|
1130 |
Rule_Def.Repeat{id = "collect_bdv", preconds = [],
|
walther@60358
|
1131 |
rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord),
|
walther@60358
|
1132 |
erls = Rule_Set.empty,srls = Rule_Set.Empty,
|
walther@60358
|
1133 |
calc = [], errpatts = [],
|
walther@60358
|
1134 |
rules = [\<^rule_thm>\<open>bdv_collect_1\<close>,
|
walther@60358
|
1135 |
\<^rule_thm>\<open>bdv_collect_2\<close>,
|
walther@60358
|
1136 |
\<^rule_thm>\<open>bdv_collect_3\<close>,
|
walther@60358
|
1137 |
|
walther@60358
|
1138 |
\<^rule_thm>\<open>bdv_collect_assoc1_1\<close>,
|
walther@60358
|
1139 |
\<^rule_thm>\<open>bdv_collect_assoc1_2\<close>,
|
walther@60358
|
1140 |
\<^rule_thm>\<open>bdv_collect_assoc1_3\<close>,
|
walther@60358
|
1141 |
|
walther@60358
|
1142 |
\<^rule_thm>\<open>bdv_collect_assoc2_1\<close>,
|
walther@60358
|
1143 |
\<^rule_thm>\<open>bdv_collect_assoc2_2\<close>,
|
walther@60358
|
1144 |
\<^rule_thm>\<open>bdv_collect_assoc2_3\<close>,
|
walther@60358
|
1145 |
|
walther@60358
|
1146 |
|
walther@60358
|
1147 |
\<^rule_thm>\<open>bdv_n_collect_1\<close>,
|
walther@60358
|
1148 |
\<^rule_thm>\<open>bdv_n_collect_2\<close>,
|
walther@60358
|
1149 |
\<^rule_thm>\<open>bdv_n_collect_3\<close>,
|
walther@60358
|
1150 |
|
walther@60358
|
1151 |
\<^rule_thm>\<open>bdv_n_collect_assoc1_1\<close>,
|
walther@60358
|
1152 |
\<^rule_thm>\<open>bdv_n_collect_assoc1_2\<close>,
|
walther@60358
|
1153 |
\<^rule_thm>\<open>bdv_n_collect_assoc1_3\<close>,
|
walther@60358
|
1154 |
|
walther@60358
|
1155 |
\<^rule_thm>\<open>bdv_n_collect_assoc2_1\<close>,
|
walther@60358
|
1156 |
\<^rule_thm>\<open>bdv_n_collect_assoc2_2\<close>,
|
walther@60358
|
1157 |
\<^rule_thm>\<open>bdv_n_collect_assoc2_3\<close>],
|
walther@60358
|
1158 |
scr = Rule.Empty_Prog});
|
neuper@37954
|
1159 |
|
wneuper@59472
|
1160 |
\<close>
|
wneuper@59472
|
1161 |
ML\<open>
|
neuper@37954
|
1162 |
(*.transforms an arbitrary term without roots to a polynomial [4]
|
neuper@37954
|
1163 |
according to knowledge/Poly.sml.*)
|
s1210629013@55444
|
1164 |
val make_polynomial_in = prep_rls'(
|
walther@60358
|
1165 |
Rule_Set.Sequence {
|
walther@60358
|
1166 |
id = "make_polynomial_in", preconds = [], rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord),
|
walther@60358
|
1167 |
erls = Atools_erls, srls = Rule_Set.Empty, calc = [], errpatts = [],
|
walther@60358
|
1168 |
rules = [
|
walther@60358
|
1169 |
Rule.Rls_ expand_poly,
|
walther@60358
|
1170 |
Rule.Rls_ order_add_mult_in,
|
walther@60358
|
1171 |
Rule.Rls_ simplify_power,
|
walther@60358
|
1172 |
Rule.Rls_ collect_numerals,
|
walther@60358
|
1173 |
Rule.Rls_ reduce_012,
|
walther@60358
|
1174 |
\<^rule_thm>\<open>realpow_oneI\<close>,
|
walther@60358
|
1175 |
Rule.Rls_ discard_parentheses,
|
walther@60358
|
1176 |
Rule.Rls_ collect_bdv],
|
walther@60358
|
1177 |
scr = Rule.Empty_Prog});
|
neuper@37954
|
1178 |
|
wneuper@59472
|
1179 |
\<close>
|
wneuper@59472
|
1180 |
ML\<open>
|
walther@60358
|
1181 |
val separate_bdvs = Rule_Set.append_rules "separate_bdvs" collect_bdv [
|
walther@60358
|
1182 |
\<^rule_thm>\<open>separate_bdv\<close>, (*"?a * ?bdv / ?b = ?a / ?b * ?bdv"*)
|
walther@60358
|
1183 |
\<^rule_thm>\<open>separate_bdv_n\<close>,
|
walther@60358
|
1184 |
\<^rule_thm>\<open>separate_1_bdv\<close>, (*"?bdv / ?b = (1 / ?b) * ?bdv"*)
|
walther@60358
|
1185 |
\<^rule_thm>\<open>separate_1_bdv_n\<close>, (*"?bdv \<up> ?n / ?b = 1 / ?b * ?bdv \<up> ?n"*)
|
walther@60358
|
1186 |
\<^rule_thm>\<open>add_divide_distrib\<close> (*"(?x + ?y) / ?z = ?x / ?z + ?y / ?z"
|
walther@60358
|
1187 |
WN051031 DOES NOT BELONG TO HERE*)];
|
wneuper@59472
|
1188 |
\<close>
|
wneuper@59472
|
1189 |
ML\<open>
|
s1210629013@55444
|
1190 |
val make_ratpoly_in = prep_rls'(
|
walther@60358
|
1191 |
Rule_Set.Sequence {
|
walther@60358
|
1192 |
id = "make_ratpoly_in", preconds = []:term list, rew_ord = ("dummy_ord", Rewrite_Ord.dummy_ord),
|
walther@60358
|
1193 |
erls = Atools_erls, srls = Rule_Set.Empty, calc = [], errpatts = [],
|
walther@60358
|
1194 |
rules = [
|
walther@60358
|
1195 |
Rule.Rls_ norm_Rational,
|
walther@60358
|
1196 |
Rule.Rls_ order_add_mult_in,
|
walther@60358
|
1197 |
Rule.Rls_ discard_parentheses,
|
walther@60358
|
1198 |
Rule.Rls_ separate_bdvs,
|
walther@60358
|
1199 |
(* Rule.Rls_ rearrange_assoc, WN060916 why does cancel_p not work?*)
|
walther@60358
|
1200 |
Rule.Rls_ cancel_p
|
walther@60358
|
1201 |
(*\<^rule_eval>\<open>divide\<close> (eval_cancel "#divide_e") too weak!*)],
|
walther@60358
|
1202 |
scr = Rule.Empty_Prog});
|
wneuper@59472
|
1203 |
\<close>
|
wenzelm@60289
|
1204 |
rule_set_knowledge
|
wenzelm@60286
|
1205 |
order_add_mult_in = order_add_mult_in and
|
wenzelm@60286
|
1206 |
collect_bdv = collect_bdv and
|
wenzelm@60286
|
1207 |
make_polynomial_in = make_polynomial_in and
|
wenzelm@60286
|
1208 |
make_ratpoly_in = make_ratpoly_in and
|
wenzelm@60286
|
1209 |
separate_bdvs = separate_bdvs
|
wenzelm@60286
|
1210 |
ML \<open>
|
walther@60278
|
1211 |
\<close> ML \<open>
|
walther@60278
|
1212 |
\<close> ML \<open>
|
walther@60278
|
1213 |
\<close>
|
neuper@37906
|
1214 |
end
|
neuper@37906
|
1215 |
|
neuper@37906
|
1216 |
|
neuper@37906
|
1217 |
|
neuper@37906
|
1218 |
|
neuper@37906
|
1219 |
|
neuper@37906
|
1220 |
|