Singular Manual: exteriorBasis

| #### D.3.1.29 exteriorBasis Procedure from library `matrix.lib` (see matrix_lib). Return: qring, an exterior algebra containing the ideal "extBasis", being a basis of the k-th exterior power of an n-dim vector space. Note: The output polynomial ring has characteristics 0 and n variables named "S(i)", where the base variable name S is either given by the optional string argument(which must not contain brackets) or equal to "e" by default. Example:
    LIB "matrix.lib";
    // basis of the 3-rd symmetricPower of a 4-dim vector space:
    def r = exteriorBasis(4, 3, "@e"); setring r;
    r; // container ring:
    ==> // coefficients: QQ
    ==> // number of vars : 4
    ==> //        block   1 : ordering dp
    ==> //                  : names    @e(1) @e(2) @e(3) @e(4)
    ==> //        block   2 : ordering C
    ==> // noncommutative relations:
    ==> //    @e(2)@e(1)=-@e(1)*@e(2)
    ==> //    @e(3)@e(1)=-@e(1)*@e(3)
    ==> //    @e(4)@e(1)=-@e(1)*@e(4)
    ==> //    @e(3)@e(2)=-@e(2)*@e(3)
    ==> //    @e(4)@e(2)=-@e(2)*@e(4)
    ==> //    @e(4)@e(3)=-@e(3)*@e(4)
    ==> // quotient ring from ideal
    ==> _[1]=@e(4)^2
    ==> _[2]=@e(3)^2
    ==> _[3]=@e(2)^2
    ==> _[4]=@e(1)^2
    extBasis; // exterior basis:
    ==> extBasis[1]=@e(2)*@e(3)*@e(4)
    ==> extBasis[2]=@e(1)*@e(3)*@e(4)
    ==> extBasis[3]=@e(1)*@e(2)*@e(4)
    ==> extBasis[4]=@e(1)*@e(2)*@e(3)
See also: symmetricBasis.

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