ApCoCoA-1:NC.Add
Gbmr.MRAdd
Addition of two polynomials over a monoid ring.
Syntax
Gbmr.MRAdd(X:STRING, Ordering:STRING, R:LIST, F1:LIST, F2:LIST):LIST
Description
Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.
@param X: an finite set of letters. It is of STRING type. Notice that every letter in X MUST appear only once.The order of letters in X is very important, since it induces a term ordering.
@param Ordering: a term ordering induced by the order of letters in X. It is represented as a STRING, which is a shortened-form of a name of corresponding term ordering. Notice that "LLEX" (length-lexicographic ordering) and "ELIM" (elimination ordering) are the only orderings supported currently.
@param R: a finite set of relations and it is of LIST type. Each element in R has form [w_{l}, w_{r}], where w_{l} and w_{r} are terms in M. Each term is represented as a STRING. For example, xy^2x is represented as "xyyx", identity element is represented as an empty STRING "", and relation (yx, xy) is represented as ["yx", "xy"].
@param F1, F2: two polynomials, where are left and right operands of addition respectively. Each polynomial is represented as a LIST of LISTs, which are pairs of form [a_{i}, w_{i}]. For example, polynomial F:=xy-y+1 is represented as F:=[[1,"xy"], [-1, "y"], [1,""]]. Zero polynomial is represented as an empty LIST [].
@return: a LIST which represents a polynomial equal to F1+F2.
Example
X := <quotes>abc</quotes>; Ordering := <quotes>LLEX</quotes>; Relations := [[<quotes>aa</quotes>,<quotes></quotes>], [<quotes>bb</quotes>,<quotes></quotes>], [<quotes>ab</quotes>,<quotes>c</quotes>], [<quotes>ac</quotes>, <quotes>b</quotes>], [<quotes>cb</quotes>, <quotes>a</quotes>]]; F1 := []; -- F1=0 F2 := []; -- F2=0 Gbmr.MRAdd(X, Ordering, Relations, F1,F2); ERROR: Undefined indeterminate e CONTEXT: $cocoa5.PrintTime(1 * e - 05) ------------------------------- [ ] ------------------------------- X := <quotes>abc</quotes>; Ordering := <quotes>LLEX</quotes>; Relations := [[<quotes>aa</quotes>,<quotes></quotes>], [<quotes>bb</quotes>,<quotes></quotes>], [<quotes>ab</quotes>,<quotes>c</quotes>], [<quotes>ac</quotes>, <quotes>b</quotes>], [<quotes>cb</quotes>, <quotes>a</quotes>]]; F1 := []; -- F1=0 F2 := [[1,<quotes>b</quotes>],[1,<quotes>ba</quotes>]]; -- F2=b+ba Gbmr.MRAdd(X, Ordering, Relations, F1,F2); ERROR: Undefined indeterminate e CONTEXT: $cocoa5.PrintTime(33 / 10 * e - 05) ------------------------------- [[1, <quotes>ba</quotes>], [1, <quotes>b</quotes>]] ------------------------------- X := <quotes>abc</quotes>; Ordering := <quotes>LLEX</quotes>; Relations := [[<quotes>aa</quotes>,<quotes></quotes>], [<quotes>bb</quotes>,<quotes></quotes>], [<quotes>ab</quotes>,<quotes>c</quotes>], [<quotes>ac</quotes>, <quotes>b</quotes>], [<quotes>cb</quotes>, <quotes>a</quotes>]]; F1 := [[1,<quotes>a</quotes>],[1,<quotes></quotes>]]; -- F1=a+1 F2 := [[1,<quotes>b</quotes>],[1,<quotes>ac</quotes>]]; -- F2=b+ac=2b Gbmr.MRAdd(X, Ordering, Relations, F1,F2); ERROR: Undefined indeterminate e CONTEXT: $cocoa5.PrintTime(24 / 10 * e - 05) ------------------------------- [[1, <quotes>a</quotes>], [2, <quotes>b</quotes>], [1, <quotes></quotes>]] -------------------------------
See also
