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schur.m2
needsPackage "SchurRings" A = schurRing(symbol s,4) f = s_{1} assert( f*f == s_{2} + s_{1,1} ) assert( dim s_{1,1} == 6 ) assert( dim s_{2} == 10 ) B = schurRing(s, 7) f = s_{1} assert( f*f == s_{2} + s_{1,1} ) g = f^3 expression g listForm g g1 = sum apply(listForm g, a -> a#1 * s_(a#0)) assert(g == g1) needsPackage "SchurRings" debug SchurRings debug Core B = schurRing(s, 7) f = s_{3,3,2,1,0} g = f^3 expression g exponents g; oo/print; size g assert((dim f)^3 == dim g) f = s_{2,1} + s_{1} g = f^2 assert(listForm g == {({4, 2}, 1), ({4, 1, 1}, 1), ({3, 3}, 1), ({3, 2, 1}, 2), ({3, 1, 1, 1}, 1), ({3, 1}, 2), ({2, 2, 2}, 1), ({2, 2, 1, 1}, 1), ({2, 2}, 2), ({2, 1, 1}, 2), ({2}, 1), ({1, 1}, 1)}) g1 = sum apply(listForm g, a -> a#1 * s_(a#0)) assert(g1 == g) g1-g assert(dim (g1-g) == 0) assert(dim g == (dim f)^2) exponents f 3*f -- The following do not work, as the ring is not considered as a polynomial ring assert try leadTerm (3*f) else true assert try terms f^2 else true assert try coefficients f else true assert try someTerms(f^2,2,3) else true h = s_{231223123,4534324,21312} -- The following is too large for the current algorithm -- dim h assert(s_(first exponents h) == h) end -- Local Variables: -- compile-command: "make -C $M2BUILDDIR/Macaulay2/packages/Macaulay2Doc/test schur.out" -- End: