Macaulay2 » Documentation
Packages » SchurRings :: EHPVariables
next | previous | forward | backward | up | index | toc

EHPVariables -- Specifies sequence of symbols representing e-, h-, and p-functions

Description

This is an optional argument for the constructor of a Symmetric or Schur ring. It indicates the symbols to be used to denote e-, h-, and p-functions in the associated Symmetric ring. The default values are (e,h,p).

i1 : S = schurRing(QQ,s,4,EHPVariables => (getSymbol"a",getSymbol"b",getSymbol"c"));
 
i2 : R = symmetricRing S

o2 = R

o2 : PolynomialRing
 
i3 : epol = toE s_{2,2,2}

      2
o3 = a  - a a
      3    2 4

o3 : R
 
i4 : toS epol

o4 = s
      2,2,2

o4 : S

The three symbols become the polynomial-ring generators of the associated symmetricRing. With the default (e,h,p), inspecting gens shows all three families indexed by 1..n:

i5 : R = symmetricRing(QQ,3);
 
i6 : gens R

o6 = {e , e , e , p , p , p , h , h , h }
       1   2   3   1   2   3   1   2   3

o6 : List

A custom triple works the same way. Below, a_i, c_i, b_i correspond respectively to the elementary, power-sum and complete homogeneous symmetric functions in the associated Symmetric ring:

i7 : S2 = schurRing(QQ,s,4,EHPVariables => (getSymbol"a",getSymbol"b",getSymbol"c"));
 
i8 : R2 = symmetricRing S2;
 
i9 : gens R2

o9 = {a , a , a , a , c , c , c , c , b , b , b , b }
       1   2   3   4   1   2   3   4   1   2   3   4

o9 : List

The option propagates across tensor products of Schur rings, so each factor may carry its own e/h/p alphabet without name clashes:

i10 : A = schurRing(QQ,sa,3,EHPVariables => (getSymbol"ea",getSymbol"ha",getSymbol"pa"));
 
i11 : B = schurRing(A,sb,2,EHPVariables => (getSymbol"eb",getSymbol"hb",getSymbol"pb"));
 
i12 : schurLevel B

o12 = 2

See also

Functions with optional argument named EHPVariables:

  • schurRing(...,EHPVariables=>...)
  • symmetricRing(...,EHPVariables=>...)

For the programmer

The object EHPVariables is a symbol.

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/SchurRings.m2:7819:0.