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yap-6.3/CHR/chr/examples/examples-lim2.math
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% From lim@scorpio Thu Jun 17 14:09:36 1993
% adapted for CHRs by thom fruehwirth 930617
% fourier very slow, maybe loops with beale/1, opt1/1 loops, opt2/1 works
rmin(E):- M=:=E. % thom: no optimisation
rmax(E):- (-M)=:=E. % thom: no optimisation
%
beale([X1,X2,X3,X4,X5,X6,X7]) :-
X1 + 1/4 * X4 - 8 * X5 - X6 + 9 * X7 =:= 0,
X2 + 1/2 * X4 - 12 * X5 - 1/2 * X6 + 3 * X7 =:= 0,
X3 + X6 =:= 1,
X1 >= 0,
X2 >= 0,
X3 >= 0,
X4 >= 0,
X5 >= 0,
X6 >= 0,
X7 >= 0,
rmin( - 3/4 * X4 + 20 * X5 - 1/2 * X6 + 6* X7).
% topb(L,n)
topb(L,N) :-
topb1([],L,0,N).
topb1(Li,Li,I,I) :- !.
topb1(Li,Lo,I,N) :-
insertb(P,Li,Lt),
J is I+1,
putcons(Lt,1,J),
topb1(Lt,Lo,J,N).
insertb(P,[],[P]).
insertb(P,[A|B],[P,A|B]).
insertb(P,[A|B],[A|C]) :-
insertb(P,B,C).
putcons(_,M,N) :-
M > N,
!.
putcons([P|R],M,N) :-
M0 is M - 1,
% bwriteln(P > M0/N),
% bwriteln(P < M/N),
P > M0/N,
P < M/N,
M1 is M + 1,
putcons(R,M1,N).
bwriteln(X) :-
writeln(X).
bwriteln(X) :-
writeln(delete(X)).
% may loop
fib(0,1).
fib(1,1).
fib(N,Z) :-
Z =:= X1 + X2,
N1 =:= N-1,
N2 =:= N-2,
fib(N1,X1),
fib(N2,X2).
laplace([_, _]) :- !.
laplace([H1, H2, H3|T]):-
laplace_vec(H1, H2, H3),
laplace([H2, H3|T]).
laplace_vec([_, _], [_, _], [_, _]) :- !.
laplace_vec([_TL, T, TR|T1], [ML, M, MR|T2], [_BL, B, BR|T3]):-
B + T + ML + MR - 4 * M =:= 0,
laplace_vec([T, TR|T1], [M, MR|T2], [B, BR|T3]).
%
laplace5(M) :-
M = [
[0,0,0,0,0],
[100,R,S,T,100],
[100,U,V,W,100],
[100,X,Y,Z,100],
[100,100,100,100,100]
],
laplace(M).
% [chipc]: laplace7(X).
%
% X = [[0, 0, 0, 0, 0, 0, 0], [100, (5260/99), (63625/1716), (42545/1287), (63625/1716), (5260/99), 100], [100, (388405/5148), (2050/33), (149485/2574), (2050/33), (388405/5148), 100], [100, (1125/13), (2025/26), (75), (2025/26), (1125/13), 100], [100, (477845/5148), (2900/33), (221765/2574), (2900/33), (477845/5148), 100], [100, (9590/99), (162425/1716), (120805/1287), (162425/1716), (9590/99), 100], [100, 100, 100, 100, 100, 100, 100]]
%
laplace7(M) :-
M = [
[0,0,0,0,0,0,0],
[100,R11,R12,R13,R14,R15,100],
[100,R21,R22,R23,R24,R25,100],
[100,R31,R32,R33,R34,R35,100],
[100,R41,R42,R43,R44,R45,100],
[100,R51,R52,R53,R54,R55,100],
[100,100,100,100,100,100,100]
],
laplace(M).
% [chipc]: chipOpt(X,Y,Z).
%
% X = (8/5)
% Y = (6/5)
% Z = (14/5)
%
chipOpt(X1,X2,X3) :-
X1 + 2 * X2 =< 4,
3 * X1 + X2 =< 6,
X3 =:= X1 + X2,
rmax(X3).
% chipfact(n,1,N)
chipfact(X,Y,M) :-
X =:= 0,
!,
Y =:= M.
chipfact(X,Y,M) :-
X1 =:= X - 1,
M1 =:= X * Y,
chipfact(X1,M1,M).
% order of magnitude slower than chipfact/3
fact(0,1).
fact(1,1).
fact(N,R) :- 1 < N, N =< R, M =:= N-1, fact(M,T), R =:= N * T.
%
mg(P,T,I,B,MP):-
T > 0,
T =< 1,
B + MP =:= P * (1 + I/100).
mg(P,T,I,B,MP):-
T > 1,
I1 =:= I / 100,
T1 =:= T -1,
P2 =:= P * (1 + I1) - MP,
mg(P2, T1, I, B, MP).
mg1(X,Y,Z) :-
2 =:= T,
1 =:= I,
T > 1,
I1 =:= I / 100,
T1 =:= T -1,
P2 =:= P * (1 + I1) - MP,
T1 > 0,
T1 =< 1,
B + MP =:= P2 * (1 + I/100).
% [chipc]: top0(X,Y,Z).
%
% X = _r94
% Y = (-9462212541120451001/1000000000000000000) * _r94 + (10462212541120451001/1000000000000000000) * _r90
% Z = (101/100) * _r94 + (-1) * _r90 More? (;)
%
% ---------------------------------------------------------
% [chipc]: top1(X,Y,Z).
%
% X = _r94
% Y = (-101/100) * _r94 + (201/100) * _r90
% Z = (101/100) * _r94 + (-1) * _r90 More? (;)
% ---------------------------------------------------------
% [chipc]: top(X,Y,Z).
%
% X = _r94
% Y = (-2101900399479668244827490915525641902001/100000000000000000000000000000000000000) * _r94 + (2201900399479668244827490915525641902001/100000000000000000000000000000000000000) * _r90
% Z = (101/100) * _r94 + (-1) * _r90 More? (;)
%
%
top0(P, B, MP) :- mg(P,10,1,B,MP).
top1(P, B, MP) :- mg(P,2,1,B,MP).
top(P, B, MP) :- mg(P,20,1,B,MP).
% Detection of Implied Equalities -------------------------------------------
%
top4([A,B,C,D]) :-
A=<B,
B=<C,
C=<D,
A>=D.
% B = A,
% C = A,
% D = A
/*
L = [A_m108, B_m128, C_m336, D_m660]
Constraints:
eq0([B_m128 * 1, D_m660 * -1], 0)
eq0([C_m336 * 1, D_m660 * -1], 0)
eq0([A_m108 * -1, D_m660 * 1], 0)
*/
%
% X = [(1/3), (0), (13/3)]
%
%
opt1([X1,X2,X3]) :-
X1 + X2 + 2 * X3 =< 9,
X1 + X2 - X3 =< 2,
-X1 + X2 + X3 =< 4,
X1 >= 0,
X2 >= 0,
X3 >= 0,
rmin(X1 + X2 - 4 * X3).
%
% X = [(0), (0)]
%
%
opt2([X1,X2]) :-
X1 + 2 * X2 =< 4,
X2 =< 1,
X1 >= 0,
X2 >= 0,
rmin(X1 + X2).
available_res(10).
available_res(14).
available_res(27).
available_res(60).
available_res(100).
available_cell(10).
available_cell(20).
ohm(V,I,R) :-
% bwriteln(V =:= I * R),
V =:= I * R.
sum([],Z) :-
% bwriteln(Z =:= 0),
Z =:= 0.
sum([H|T],N) :-
% bwriteln(N =:= H + M),
N =:= H + M,
sum(T,M).
kirchoff(L) :-
sum(L,0).
% X = [(200/37), (540/37)] More? (;)
%
% X = [(140/37), (600/37)] More? (;)
%
% X = [(540/127), (2000/127)] More? (;)
%
ohm_example([V1,V2]) :-
29/2 < V2, V2 < 65/4,
available_res(R1),
available_res(R2),
available_cell(V),
ohm(V1,I1,R1), ohm(V2,I2,R2),
kirchoff([I1,-I2]), kirchoff([-V,V1,V2]).
% X = [10, 27, 20] More? (;)
%
% X = [14, 60, 20] More? (;)
%
% X = [27, 100, 20] More? (;)
%
ohm_example1([R1,R2,V]) :-
29/2 < V2, V2 < 65/4,
available_res(R1),
available_res(R2),
available_cell(V),
ohm(V1,I1,R1), ohm(V2,I2,R2),
kirchoff([I1,-I2]), kirchoff([-V,V1,V2]).
%
% X = [(14), (60), (20)]
%
%
ohm1([A,B,C]) :-
A =:= 14,
B =:= 60,
C =:= 20,
29/2 < V2, V2 < 65/4,
V1/A - V2/B =:= 0,
V1 + V2 =:= C.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
example( [X0,X1,X2,X3,X4]) :-
87*X0 +52*X1 +27*X2 -54*X3 +56*X4 =< -93,
33*X0 -10*X1 +61*X2 -28*X3 -29*X4 =< 63,
-68*X0 +8*X1 +35*X2 +68*X3 +35*X4 =< -85,
90*X0 +60*X1 -76*X2 -53*X3 +24*X4 =< -68,
-95*X0 -10*X1 +64*X2 +76*X3 -24*X4 =< 33,
43*X0 -22*X1 +67*X2 -68*X3 -92*X4 =< -97,
39*X0 +7*X1 +62*X2 +54*X3 -26*X4 =< -27,
48*X0 -13*X1 +7*X2 -61*X3 -59*X4 =< -2,
49*X0 -23*X1 -31*X2 -76*X3 +27*X4 =< 3,
-50*X0 +58*X1 -1*X2 +57*X3 +20*X4 =< 6,
-13*X0 -63*X1 +81*X2 -3*X3 +70*X4 =< 64,
20*X0 +67*X1 -23*X2 -41*X3 -66*X4 =< 52,
-81*X0 -44*X1 +19*X2 -22*X3 -73*X4 =< -17,
-43*X0 -9*X1 +14*X2 +27*X3 +40*X4 =< 39,
16*X0 +83*X1 +89*X2 +25*X3 +55*X4 =< 36,
+2*X0 +40*X1 +65*X2 +59*X3 -32*X4 =< 13,
-65*X0 -11*X1 +10*X2 -13*X3 +91*X4 =< 49,
93*X0 -73*X1 +91*X2 -1*X3 +23*X4 =< -87.
top2 :- example( [X0,X1,X2,X3,X4]).
% X3<=-5/4-35/68*X2-2/17*X1+X0-35/68*X4,
% X3<=68/53-76/53*X2+60/53*X1+90/53*X0+24/53*X4,
% X3<=-1/2-31/27*X2-7/54*X1-13/18*X0+13/27*X4,
% X3<=17/22+19/22*X2-2*X1-81/22*X0-73/22*X4,
% X3<=33/76-16/19*X2+5/38*X1+5/4*X0+6/19*X4,
% X3>=87+91*X2-73*X1+93*X0+23*X4,
% X3>=-3/76-31/76*X2-23/76*X1+49/76*X0+27/76*X4,
% X3<=13/9-14/27*X2+1/3*X1+43/27*X0-40/27*X4,
% X3<=2/19+1/57*X2-58/57*X1+50/57*X0-20/57*X4
top3 :- example( [X0,_,_,_,X4]).
% X0>=477804/40409+6973307/969816*X4,
% X0>=7357764/4517605-5006476/13552815*X4,
% X0>=58416/36205-4659804/12418315*X4,
% X0>=3139326/1972045-745308/1972045*X4,
% X0>=67158/43105-16394/43105*X4,
% X0>=1327097/6210451-2619277/6210451*X4,
% X0<=-688135/1217232-2174029/811488*X4
% [chipc]: top5(X).
%
% X = [(0), (0), (0), (1000), (0), (0), (50), (200/9) + (-1/9) * _rp522 , (1000/3), (5350/9) + (1/9) * _rp522 , (4000), (0), (7450/3), (0), (0), (5000), (250), (600), (1000/9) + (-5/9) * _rp522 , (0)]
% yes.
top5([X11,X12,X13,X14,X15,X21,X22,X23,X24,X25,Y21,Y22,Y23,Y24,Y25,Z21,Z22,Z23,Z24,Z25]) :-
X11 + X12 + X13 + X14 + X15 =:= 1000,
X21 + X22 + X23 + X24 + X25 =:= 1000,
4*X11 + 5*X21 - Y21 - Z21 =< 0,
-4*X12 - 5*X22 + Y22 + Z22 =:= 0,
-4*X13 - 5*X23 + Y24 - Y25 + Z24 - Z25 =:= 0,
-4*X14 - 5*X24 + Y21 - Y22 - Y23 + Y25
+ Z21 - Z22 - Z23 + Z25 =:= 0,
-4*X15 - 5*X25 + Y23 - Y24 + Z23 - Z24 =:= 0,
7*X11 + 9*X21 >= 0,
7*X12 + 9*X22 =< 3000,
7*X13 + 9*X23 =< 200,
7*X14 + 9*X24 =< 10000,
7*X15 + 9*X25 =< 7000,
Z21 =< 5000,
Z22 =< 250,
Z23 =< 600,
Z24 =< 7000,
Z25 =< 4000,
X11 >= 0,
X12 >= 0,
X13 >= 0,
X14 >= 0,
X15 >= 0,
X21 >= 0, X22 >= 0, X23 >= 0, X24 >= 0, X25 >= 0,
Y21 >= 0, Y22 >= 0, Y23 >= 0, Y24 >= 0, Y25 >= 0,
Z21 >= 0, Z22 >= 0, Z23 >= 0, Z24 >= 0, Z25 >= 0,
M =:= 99999,
- Min =:= 99999 * X11 + 99999 * X21 + 4 * Y21 + 7 * Y22 +
3 * Y23 + 8*Y24 + 5*Y25,
rmax(Min).
%
top5a(List) :-
List = [X11,X12,X13,X14,X15,X21,X22,X23,X24,X25,Y21,Y22,Y23,Y24,Y25,Z21,Z22,Z23,Z24,Z25],
X11 + X12 + X13 + X14 + X15 =:= 1000,
X21 + X22 + X23 + X24 + X25 =:= 1000,
4*X11 + 5*X21 - Y21 - Z21 =< 0,
-4*X12 - 5*X22 + Y22 + Z22 =:= 0,
-4*X13 - 5*X23 + Y24 - Y25 + Z24 - Z25 =:= 0,
-4*X14 - 5*X24 + Y21 - Y22 - Y23 + Y25
+ Z21 - Z22 - Z23 + Z25 =:= 0,
-4*X15 - 5*X25 + Y23 - Y24 + Z23 - Z24 =:= 0,
7*X11 + 9*X21 >= 0,
7*X12 + 9*X22 =< 3000,
7*X13 + 9*X23 =< 200,
7*X14 + 9*X24 =< 10000,
7*X15 + 9*X25 =< 7000,
Z21 =< 5000,
Z22 =< 250,
Z23 =< 600,
Z24 =< 7000,
Z25 =< 4000,
X11 >= 0,
X12 >= 0,
X13 >= 0,
X14 >= 0,
X15 >= 0,
X21 >= 0, X22 >= 0, X23 >= 0, X24 >= 0, X25 >= 0,
Y21 >= 0, Y22 >= 0, Y23 >= 0, Y24 >= 0, Y25 >= 0,
Z21 >= 0, Z22 >= 0, Z23 >= 0, Z24 >= 0, Z25 >= 0,
M =:= 99999,
Min = 23450,
- Min =:= 99999 * X11 + 99999 * X21 + 4 * Y21 + 7 * Y22 +
3 * Y23 + 8*Y24 + 5*Y25.
% M = 99999,
% Min = 23450,
% X11 = 0,
% X12 = 0,
% X13 = 0,
% X14 = 1000,
% X15 = 0,
% X21 = 0,
% X22 = 50,
% X23 = 1850/3-X25,
% X24 = 1000/3,
% Y21 = 4000,
% Y22 = 0,
% Y23 = 7450/3,
% Y24 = 0,
% Y25 = 0,
% Z21 = 5000,
% Z22 = 250,
% Z23 = 600,
% Z24 = 9250/3-5*X25,
% Z25 = 0,
% X25>=5350/9,
% X25<=1850/3
% ===========================================================================
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