diff options
Diffstat (limited to 'src/algebra/newpoly.spad.pamphlet')
| -rw-r--r-- | src/algebra/newpoly.spad.pamphlet | 18 |
1 files changed, 5 insertions, 13 deletions
diff --git a/src/algebra/newpoly.spad.pamphlet b/src/algebra/newpoly.spad.pamphlet index 23cd07b7..88fb5070 100644 --- a/src/algebra/newpoly.spad.pamphlet +++ b/src/algebra/newpoly.spad.pamphlet @@ -1029,13 +1029,9 @@ RecursivePolynomialCategory(R:Ring, E:OrderedAbelianMonoidSup, V:OrderedSet): Ca if R has IntegralDomain then - if R has EuclideanDomain - then - exactQuo(r:R,s:R):R == - r quo$R s - else - exactQuo(r:R,s:R):R == - (r exquo$R s)::R + exactQuo(r:R,s:R):R == + R has EuclideanDomain => r quo$R s + (r exquo$R s)::R exactQuotient (p:$,r:R) == (p exquo$$ r)::$ @@ -1215,9 +1211,7 @@ RecursivePolynomialCategory(R:Ring, E:OrderedAbelianMonoidSup, V:OrderedSet): Ca mpc2Z := MPolyCatFunctions2(Symbol,IES,IES,Z,R,PZ,PR) mpc2Q := MPolyCatFunctions2(Symbol,IES,IES,Q,R,PQ,PR) - ZToR (z:Z):R == coerce(z)@R QToR (q:Q):R == coerce(q)@R - PZToPR (pz:PZ):PR == map(ZToR,pz)$mpc2Z PQToPR (pq:PQ):PR == map(QToR,pq)$mpc2Q retract(pz:PZ) == @@ -1254,7 +1248,7 @@ RecursivePolynomialCategory(R:Ring, E:OrderedAbelianMonoidSup, V:OrderedSet): Ca retractIfCan(pr)@Union($,"failed") retractIfCan(pz:PZ) == - pr : PR := PZToPR(pz) + pr : PR := map(#1::R,pz)$mpc2Z retractIfCan(pr)@Union($,"failed") retract(pr:PR) == @@ -1298,8 +1292,6 @@ RecursivePolynomialCategory(R:Ring, E:OrderedAbelianMonoidSup, V:OrderedSet): Ca then mpc2Z := MPolyCatFunctions2(Symbol,IES,IES,Z,R,PZ,PR) - ZToR (z:Z):R == coerce(z)@R - PZToPR (pz:PZ):PR == map(ZToR,pz)$mpc2Z retract(pz:PZ) == rif : Union($,"failed") := retractIfCan(pz)@Union($,"failed") @@ -1323,7 +1315,7 @@ RecursivePolynomialCategory(R:Ring, E:OrderedAbelianMonoidSup, V:OrderedSet): Ca localRetractIfCanPZ(pz)@Union($,"failed") else retractIfCan(pz:PZ) == - pr : PR := PZToPR(pz) + pr : PR := map(#1::R,pz)$mpc2Z retractIfCan(pr)@Union($,"failed") retract(pr:PR) == |