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# Littlewood-Richardson Calculator
# Copyright (C) 1999- Anders S. Buch (asbuch at math rutgers edu)
# See the file LICENSE for license information.
tos := proc(expr)
local i, res, term, base, expo;
if _iss(expr) then
i := _partlen(expr);
if i = 0 then
RETURN(1);
else
RETURN(s[op(1..i, expr)]);
fi;
elif type(expr, `+`) then
res := 0;
for term in expr do
res := res + tos(term);
od;
RETURN(res);
elif type(expr, `*`) then
res := tos(op(1, expr));
for i from 2 to nops(expr) do
res := _mults2(res * tos(op(i, expr)));
od;
RETURN(res);
elif type(expr, `^`) then
base := tos(op(1, expr));
expo := expand(op(2, expr));
if type(expo, integer) then
if expo > 1 then
while expo mod 2 = 0 do
base := _mults2(base^2);
expo := expo / 2;
od;
res := base;
expo := expo - 1;
# return res * base ^ expo
while expo > 0 do
base := _mults2(base^2);
expo := expo / 2;
if expo mod 2 = 1 then
res := _mults2(res * base);
expo := expo - 1;
fi;
od;
RETURN(res);
fi;
fi;
RETURN(base^expo);
elif type(expr, list) then
RETURN([seq(tos(expr[i]), i=1..nops(expr))]);
elif type(expr, set) then
RETURN({seq(tos(expr[i]), i=1..nops(expr))});
else
RETURN(expr);
fi;
0$0;
end:
skew := proc(expr, shape)
local ee, sh, res, term, tt, s_part, c_part, fac;
if not (type(shape, list) or _iss(shape)) then
ERROR(`second argument must be a partition`, shape);
fi;
ee := tos(expr);
sh := _partlen(shape);
if sh = 0 then
RETURN(ee);
fi;
sh := s[op(1..sh, shape)];
if not type(ee, `+`) then
ee := [ee];
fi;
res := 0;
for term in ee do
if type(term, `*`) then
tt := term;
else
tt := [term];
fi;
s_part := 1;
c_part := 1;
for fac in tt do
if _iss(fac) then
s_part := s_part * fac;
else
c_part := c_part * fac;
fi;
od;
if _iss(s_part) then
if sh = s_part then
res := res + c_part;
elif _subpart(sh, s_part) then
res := res + expand(c_part * _call_lrskew(s_part, sh));
fi;
fi;
od;
RETURN(res);
end:
lrcoef := proc(outer, inner1, inner2)
local cmd, fd, res, i;
cmd := cat(LRCALC_BIN_PATH, ` coef `,
seq(cat(` `, op(i,outer)), i=1..nops(outer)), ` -`,
seq(cat(` `, op(i,inner1)), i=1..nops(inner1)), ` -`,
seq(cat(` `, op(i,inner2)), i=1..nops(inner2)));
fd := process[popen](cmd, READ);
res := readline(fd);
process[pclose](fd);
RETURN(parse(res));
end:
_iss := proc(expr)
if not type(expr, indexed) then
RETURN(false);
fi;
RETURN(evalb(op(0, expr) = `s`));
end:
_mults2 := proc(expr)
local ee, res, term, tt, s_part, c_part, fac, base, expo;
ee := expand(expr);
if not type(ee, `+`) then
ee := [ee];
fi;
res := 0;
for term in ee do
if type(term, `*`) then
tt := term;
else
tt := [term];
fi;
s_part := 1;
c_part := 1;
for fac in tt do
if _iss(fac) then
if type(s_part, integer) then
s_part := fac;
elif _cmppart(s_part, fac) <= 0 then
s_part := _call_lrmult(s_part, fac);
else
s_part := _call_lrmult(fac, s_part);
fi;
elif type(fac, `^`) then
base := op(1, fac);
expo := op(2, fac);
if _iss(base) and expo = 2 then
s_part := s_part * _call_lrmult(base, base);
else
c_part := c_part * fac;
fi;
else
c_part := c_part * fac;
fi;
od;
res := res + expand(c_part * s_part);
od;
RETURN(res);
end:
# quantum(rows, cols) and QUANTUM_OPTS are for doing calculations in
# the quantum cohomology ring of Gr(d,n) where d=rows and n=rows+cols,
# rather than the ring of symmetric functions.
quantum := proc(rows, cols)
global QUANTUM_OPTS;
if rows <= 0 or cols <= 0 then
QUANTUM_OPTS := ``;
else
QUANTUM_OPTS := cat(` -q`, rows, `,`, cols);
fi;
readlib(forget);
forget(_call_lrmult);
0$0;
end:
fusion := proc(rows, cols)
global QUANTUM_OPTS;
if rows <= 0 or cols <= 0 then
QUANTUM_OPTS := ``;
else
QUANTUM_OPTS := cat(` -f`, rows, `,`, cols);
fi;
readlib(forget);
forget(_call_lrmult);
0$0;
end:
QUANTUM_OPTS := ``:
_call_lrmult := proc(fac1, fac2)
option remember;
local cmd, fd, res, i;
global QUANTUM_OPTS;
cmd := cat(LRCALC_BIN_PATH, ` mult -m`, QUANTUM_OPTS,
seq(cat(` `, op(i,fac1)), i=1..nops(fac1)), ` -`,
seq(cat(` `, op(i,fac2)), i=1..nops(fac2)));
fd := process[popen](cmd, READ);
res := readline(fd);
process[pclose](fd);
RETURN(parse(res));
end:
_call_lrskew := proc(outer, inner)
option remember;
local cmd, fd, res, i;
cmd := cat(LRCALC_BIN_PATH, ` skew -m`,
seq(cat(` `, op(i,outer)), i=1..nops(outer)), ` /`,
seq(cat(` `, op(i,inner)), i=1..nops(inner)));
fd := process[popen](cmd, READ);
res := readline(fd);
process[pclose](fd);
RETURN(parse(res));
end:
_partlen := proc(lambda)
local n;
n := nops(lambda);
while n > 0 and op(n,lambda) = 0 do n := n - 1; od;
RETURN(n);
end:
_cmppart := proc(p1, p2)
local n;
n := nops(p1);
if n <> nops(p2) then
RETURN(n - nops(p2));
fi;
while n > 0 do
if op(n, p1) <> op(n, p2) then
RETURN(op(n, p1) - op(n, p2));
fi;
n := n - 1;
od;
RETURN(0);
end:
_subpart := proc(p1, p2)
local n;
n := _partlen(p1);
if n > nops(p2) then
RETURN(false);
fi;
while n > 0 do
if op(n, p1) > op(n, p2) then
RETURN(false);
fi;
n := n - 1;
od;
RETURN(true);
end:
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