Singular Manual: ring operations (plural)

| #### 7.2.7.2 ring operations (plural) `+` construct a tensor product 195#195of two 190#190-algebras 191#191 and 196#196 over the ground field. Let, e.g., 197#197 198#198, and 199#199 200#200 be two 190#190-algebras, then 78#78 is defined to be the algebra 201#201 202#202, 203#203, 204#204. Concerning the ground fields 98#98 resp. 99#99 of 191#191 resp. 196#196, take the following guidelines for 205#205 into consideration: Neither 98#98 nor 99#99 may be 53#53 or 78#78. If the characteristic of 98#98 and 99#99 differs, then one of them must be 3#3. At most one of 98#98 and 99#99 may have parameters. If one of 98#98 and 99#99 is an algebraic extension of 22#22 it may not be defined by a `charstr` of type `(p^n,a)`. One can create a ring using `ring(list)`, see also `ringlist`. Example:
    LIB "ncalg.lib";
    def a = makeUsl2();       // U(sl_2) in e,f,h presentation
    ring W0 = 0,(x,d),dp;
    def W = Weyl();              // 1st Weyl algebra in x,d
    def S = a+W;
    setring S;
    S;
    ==> // coefficients: QQ considered as a field
    ==> // number of vars : 5
    ==> //        block   1 : ordering dp
    ==> //                  : names    e f h
    ==> //        block   2 : ordering dp
    ==> //                  : names    x d
    ==> //        block   3 : ordering C
    ==> // noncommutative relations:
    ==> //    fe=ef-h
    ==> //    he=eh+2e
    ==> //    hf=fh-2f
    ==> //    dx=xd+1

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