diff --git a/books/bookvol10.4.pamphlet b/books/bookvol10.4.pamphlet index 91f694d..6f640e4 100644 --- a/books/bookvol10.4.pamphlet +++ b/books/bookvol10.4.pamphlet @@ -57022,6 +57022,308 @@ ListToMap(A:SetCategory, B:Type): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{package LPARSPT LocalParametrizationOfSimplePointPackage} +<>= +)set break resume +)sys rm -f LocalParametrizationOfSimplePointPackage.output +)spool LocalParametrizationOfSimplePointPackage.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show LocalParametrizationOfSimplePointPackage +--R LocalParametrizationOfSimplePointPackage(K: Field,symb: List Symbol,PolyRing: PolynomialCategory(K,E,OrderedVariableList symb),E: DirectProductCategory(# symb,NonNegativeInteger),ProjPt: ProjectiveSpaceCategory K,PCS: LocalPowerSeriesCategory K,Plc: PlacesCategory(K,PCS)) is a package constructor +--R Abbreviation for LocalParametrizationOfSimplePointPackage is LPARSPT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.4.pamphlet to see algebra source code for LPARSPT +--R +--R------------------------------- Operations -------------------------------- +--R pointDominateBy : Plc -> ProjPt printInfo : Boolean -> Boolean +--R printInfo : () -> Boolean +--R localParamOfSimplePt : (ProjPt,PolyRing,Integer) -> List PCS +--R localize : (PolyRing,ProjPt,PolyRing,Integer) -> Record(fnc: PolyRing,crv: PolyRing,chart: List Integer) +--R pointToPlace : (ProjPt,PolyRing) -> Plc +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +LocalParametrizationOfSimplePointPackage examples +==================================================================== + +See Also: +o )show LocalParametrizationOfSimplePointPackage + +@ +\pagehead{LocalParametrizationOfSimplePointPackage}{LPARSPT} +\pagepic{ps/v104localparametrizationofsimplepointpackage.eps}{LPARSPT}{1.00} + +{\bf Exports:}\\ +\begin{tabular}{lllll} +\cross{LPARSPT}{pointDominateBy} & +\cross{LPARSPT}{printInfo} & +\cross{LPARSPT}{localParamOfSimplePt} & +\cross{LPARSPT}{localize} & +\cross{LPARSPT}{pointToPlace} +\end{tabular} + +<>= +)abbreviation package LPARSPT LocalParametrizationOfSimplePointPackage +++ Author: Gaetan Hache +++ Date Created: 17 nov 1992 +++ Date Last Updated: May 2010 by Tim Daly +++ Description: +++ The following is part of the PAFF package +LocalParametrizationOfSimplePointPackage(K,symb,PolyRing,E,ProjPt,PCS,Plc):_ + Exports == Implementation where + K:Field + symb: List(Symbol) + + E : DirectProductCategory(#symb,NonNegativeInteger) + OV ==> OrderedVariableList(symb) + + PolyRing : PolynomialCategory(K,E,OV) + ProjPt : ProjectiveSpaceCategory(K) + PCS : LocalPowerSeriesCategory(K) + Plc : PlacesCategory(K,PCS) + + PI ==> PositiveInteger + NNI ==> NonNegativeInteger + PPFC1 ==> PolynomialPackageForCurve(K,PolyRing,E,#symb,ProjPt) + PackPoly ==> PackageForPoly(K,PolyRing,E,#symb) + UP ==> SparseUnivariatePolynomial(K) + UPUP ==> SparseUnivariatePolynomial(UP) + + Exports ==> with + + printInfo: Boolean -> Boolean + ++ printInfo(b) set a flag such that when true (b <- true) prints + ++ some information during some critical computation. + + printInfo: () -> Boolean + ++ returns the value of the \spad{printInfo} flag. + + pointToPlace: (ProjPt,PolyRing) -> Plc + ++ pointToPlace(pt,pol) takes for input a simple point pt on the curve + ++ defined by pol and set the local parametrization of the point. + + localParamOfSimplePt: (ProjPt,PolyRing,Integer) -> List PCS + ++ localParamOfSimplePt(pt,pol,n) computes the local parametrization + ++ of the simple point pt on the curve defined by pol. This local + ++ parametrization is done according to the standard open affine + ++ plane set by n + + pointDominateBy : Plc -> ProjPt + ++ pointDominateBy(pl) returns the projective point dominated + ++ by the place pl. + + localize: (PolyRing,ProjPt,PolyRing,Integer) -> _ + Record(fnc:PolyRing,crv:PolyRing,chart:List(Integer)) + ++ localize(f,pt,crv,n) returns a record containing the polynomials f + ++ and crv translate to the origin with respect to pt. The last + ++ element of the records, consisting of three integers contains + ++ information about the local parameter that will be used + ++ (either x or y): the first integer correspond to the variable + ++ that will be used as a local parameter. + + Implementation ==> add + + import PCS + import PolyRing + import PPFC1 + import PackPoly + + valuationAndMore: (UPUP,UPUP) -> _ + Record(ord:Integer,value:K,fnc:UPUP,crv:UPUP) + + localize2: (PolyRing,ProjPt,PolyRing,Integer) -> _ + Record(fnc2:UPUP,crv2:UPUP) + + coerceToUPUP: (PolyRing,List Integer) -> UPUP + + paramAtOrigin: (UPUP,UPUP,Integer) -> PCS + + strictTransform: (UPUP,NNI) -> UPUP + + translate: (UPUP,K) -> UPUP + + constant: UPUP -> K + + intCoord: UPUP -> K + + localMultiplicity: UPUP -> NNI + + mapDegree: (NNI,NNI,NNI) -> NNI + + listVar:List(OV):= [index(i::PI)$OV for i in 1..#symb] + + listMonoPols:List(PolyRing):=listVariable() + + pointDominateBy(pl)== + lpl:List PCS:=localParam(pl) + empty? lpl => _ + error "LPARSPT:pointDominateBy::parametrization of point not done yet" + lK:List K:=[ findCoef(s,0) for s in lpl] + projectivePoint(lK) + + localParamOfSimplePt(pt,curve,nV)== + mult:NNI:=multiplicity(curve,pt,nV) + ^one?(mult) => _ + error "The point is not simple or is not on the curve !" + lcl:=[localize2(var,pt,curve,nV) for var in listMonoPols] + [paramAtOrigin(l.fnc2,l.crv2,0) for l in lcl] + + pointToPlace(pt,curve)== + -- define the chart for strictTransform (of simple point) + nV:Integer:=lastNonNull pt + pth:=homogenize(pt,nV) + chart:List Integer:=[0,0,nV] + mult:NNI:=multiplicity(curve,pth,nV) + ^one?(mult) => + error "The point is not simple or is not on the curve" + -- create a place from the simple point. This is done by giving + -- a name to the place: in this case it is the coordinate of + -- the projective point. + lpth:List K:= pth :: List(K) + plc:Plc:=create(lpth)$Plc + ^empty?(localParam(plc)) => plc + lcl:=[localize2(var,pth,curve,nV) for var in listMonoPols] + lPar:=[paramAtOrigin(l.fnc2,l.crv2,0) for l in lcl] + setParam!(plc,lPar) + dd:=degree pth + setDegree!(plc,dd) + plc + + localVarForPrintInfo:Boolean:=false()$Boolean + + printInfo()==localVarForPrintInfo + + printInfo(flag)==localVarForPrintInfo:=flag + + mapDegree(n,mx,m)== + dd:=(n+mx-m) + dd < 0 => _ + error "LPARSPT:mapDegree called by PARAMP:strictTransform failed" + dd pretend NNI + + strictTransform(pol,m)== + zero?(pol) => 0 + tc:=leadingCoefficient pol + tk:= degree pol + newTc:= mapExponents(mapDegree(#1,tk,m),tc) + monomial(newTc,tk)$UPUP + strictTransform(reductum pol,m) + + Y == monomial(1,1)$UPUP + + trY: (K,NonNegativeInteger) -> UPUP + trY(a,n)== (monomial(monomial(a,0)$UP,0)$UPUP + Y)**n + + translate(pol,a)== + zero?(pol) => 0 + tc:=leadingCoefficient pol + tk:= degree pol + trY(a,tk) * tc + translate(reductum pol, a) + + constant(pol)==coefficient(coefficient(pol,0)$UPUP,0)$UP + + intCoord(pol)== + coefY:=coefficient(coefficient(pol,1)$UPUP,0)$UP + cnst:=constant(pol) + -cnst * inv coefY + + localMultiplicity(pol)== + zero?(pol) => error "Cannot compute the multiplicity for 0" + redPol:= reductum pol + tc:=leadingCoefficient pol + tk:= degree pol + m:=tk + minimumDegree(tc)$UP + zero?(redPol) => m + min( m, localMultiplicity(redPol)) + + coerceToUPUP(pol,chart)== + zero?(pol) => 0 + lExp:=parts degree pol + lCoef:=leadingCoefficient pol + expX:=lExp(chart.1) + expY:=lExp(chart.2) + monomial(monomial(lCoef,expX)$UP,expY)$UPUP + _ + coerceToUPUP(reductum(pol),chart) + + -- testing this function. See paramPack for original version. + valuationAndMore(f:UPUP,curve:UPUP)== + -- this function evaluate the function f at the origin + -- which must be a simple point on the curve define by "curve" + val:= constant(f) + ^zero?(val) => [0,val,f,curve] + sTrCurve:=strictTransform(curve,1) + slp:=intCoord sTrCurve + multPtf:Integer:= localMultiplicity(f) pretend Integer + sTrFnc:=strictTransform(f,multPtf pretend NNI) + newCurve:=translate(sTrCurve,slp) + f2:=translate(sTrFnc,slp) + val:= constant(f2) + [multPtf, val, f2, newCurve] + + paramAtOrigin(f:UPUP,curve:UPUP,ex:Integer)== delay + -- this function must be + -- called for parametrization a the origin + u:=f + zero?(u) => 0 + tt:=u exquo curve + ^(tt case "failed") => 0 + firstTerm:=valuationAndMore(u,curve) + od:=firstTerm.ord + coef:=firstTerm.value + newU:=firstTerm.fnc - monomial(monomial(coef,0)$UP,0)$UPUP + newCurve:=firstTerm.crv + series(od+ex,coef,paramAtOrigin(newU,newCurve,ex+od)) + + localize(f:PolyRing,pt:ProjPt,curve:PolyRing,nV:Integer)== + curveT:=translateToOrigin(curve,pt,nV) + ft:=translateToOrigin(f,pt,nV) + fm:=minimalForm(curveT) + zero?(d:=totalDegree(fm)$PackPoly) => _ + error "the point is not on the curve" + ^one?(d) => error "the point is singular" + subChart:=[i for i in 1..#symb | ^(i= (nV pretend PI))] + cf1:=degOneCoef(fm,(subChart.1) pretend PI) + cf2:=degOneCoef(fm,(subChart.2) pretend PI) + crt:List(Integer) + sc:List(Integer):=[(i pretend Integer) for i in subChart] + zero?(cf1) => + crt:=concat(sc,nV) + [ft,curveT,crt] + zero?(cf2) => + crt:=concat(reverse(sc),nV) + [ft,curveT,crt] + deg1:=degree(curveT,listVar(subChart.1)) + deg2:=degree(curveT,listVar(subChart.2)) + deg1 > deg2 => + crt:=concat(sc,nV) + [ft,curveT,crt] + crt:=concat(reverse(sc),nV) + [ft,curveT,crt] + + localize2(f:PolyRing,pt:ProjPt,curve:PolyRing,nV:Integer)== + recBlowUp:=localize(f,pt,curve,nV) + f2:=coerceToUPUP(recBlowUp.fnc,recBlowUp.chart) + curve2:=coerceToUPUP(recBlowUp.crv,recBlowUp.chart) + [f2,curve2] + +@ +<>= +"LPARSPT" [color="#FF4488",href="bookvol10.4.pdf#nameddest=LPARSPT"] +"DIRPCAT" [color="#4488FF",href="bookvol10.2.pdf#nameddest=DIRPCAT"] +"PFECAT" [color="#4488FF",href="bookvol10.2.pdf#nameddest=PFECAT"] +"LPARSPT" -> "DIRPCAT" +"LPARSPT" -> "PFECAT" + +@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \chapter{Chapter M} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{package MKBCFUNC MakeBinaryCompiledFunction} @@ -157078,6 +157380,7 @@ ZeroDimensionalSolvePackage(R,ls,ls2): Exports == Implementation where <> <> <> +<> <> <> diff --git a/books/bookvol5.pamphlet b/books/bookvol5.pamphlet index 5c3fed1..86f50bb 100644 --- a/books/bookvol5.pamphlet +++ b/books/bookvol5.pamphlet @@ -24017,6 +24017,7 @@ otherwise the new algebra won't be loaded by the interpreter when needed. (|ListFunctions2| . LIST2) (|ListFunctions3| . LIST3) (|ListToMap| . LIST2MAP) + (|LocalParametrizationOfSimplePointPackage| . LPARSPT) (|MakeFloatCompiledFunction| . MKFLCFN) (|MakeFunction| . MKFUNC) (|MakeRecord| . 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${OUT}/FRAMALG.o ${OUT}/FRAMALG-.o ${OUT}/MDAGG.o ${OUT}/NPOLYGON.o \ + ${OUT}/FRAMALG.o ${OUT}/FRAMALG-.o ${OUT}/LPARSPT.o \ + ${OUT}/MDAGG.o ${OUT}/NPOLYGON.o \ ${OUT}/ODPOL.o ${OUT}/PLOT.o ${OUT}/RFP.o \ ${OUT}/RMCAT2.o ${OUT}/ROIRC.o ${OUT}/SDPOL.o \ ${OUT}/SMATCAT.o ${OUT}/SMATCAT-.o ${OUT}/TUBETOOL.o ${OUT}/UPXSCCA.o \ @@ -8964,7 +8966,8 @@ LAYER12=\ @ <>= /* layer 12 */ -/* depends on: DIOPS DPOLCAT FFSQFRFINRALG FRAC RMATCAT RRCC UPXSCAT */ +/* depends on: DIOPS DPOLCAT FFSQFR FINRALG FRAC RMATCAT RRCC UPXSCAT */ +/* PLPKCRV */ "DFLOAT" [color="#88FF44",href="bookvol10.3.pdf#nameddest=DFLOAT", shape=ellipse] @@ -9098,6 +9101,25 @@ LAYER12=\ /*"FRAMALG-" -> {"OAGROUP"; "OCAMON"; "OAMON"; "OASGP"; "CFCAT"; "REAL"}*/ /*"FRAMALG-" -> {"OM"; "NNI"; "PI"; "SINT"; "LIST"; "ILIST"}*/ +"LPARSPT" [color="#FF4488",href="bookvol10.4.pdf#nameddest=LPARSPT"] +"LPARSPT" -> "PLPKCRV" +/*"LPARSPT" -> {"PFECAT"; "DIRPCAT"}*/ +/*"LPARSPT" -> {"PRSPCAT"; "SETCATD"; "LOCPOWC"; "PLACESC"; "FIELD"}*/ +/*"LPARSPT" -> {"EUCDOM"; "PID"; "GCDDOM"; "INTDOM"; "COMRING"; "RING"}*/ +/*"LPARSPT" -> {"RNG"; "ABELGRP"; "CABMON"; "ABELMON"; "ABELSG"; "SETCAT"}*/ +/*"LPARSPT" -> {"BASTYPE"; "KOERCE"; "SGROUP"; "MONOID"; "LMODULE"}*/ +/*"LPARSPT" -> {"BMODULE"; "RMODULE"; "ALGEBRA"; "MODULE"; "ENTIRER"}*/ +/*"LPARSPT" -> {"UFD"; "DIVRING"; "POLYCAT"; "PDRING"; "FAMR"; "AMR"}*/ +/*"LPARSPT" -> {"CHARZ"; "CHARNZ"; "FRETRCT"; "RETRACT"; "EVALAB"}*/ +/*"LPARSPT" -> {"IEVALAB"; "FLINEXP"; "LINEXP"; "ORDSET"; "KONVERT"}*/ +/*"LPARSPT" -> {"PATMAB"; "IXAGG"; "HOAGG"; "AGG"; "TYPE"; "ELTAGG"}*/ +/*"LPARSPT" -> {"ELTAB"; "DIFEXT"; "DIFRING"; "FINITE"; "ORDRING"}*/ +/*"LPARSPT" -> {"OAGROUP"; "OCAMON"; "OAMON"; "OASGP"; "OAMONS"}*/ +/*"LPARSPT" -> {"VSPACE"; "UPSCAT"; "PSCAT"; "SINT"; "INT"; "LSAGG"}*/ +/*"LPARSPT" -> {"STAGG"; "URAGG"; "RCAGG"; "LNAGG"; "CLAGG"; "FLAGG"}*/ +/*"LPARSPT" -> {"ELAGG"; "OM"; "LIST"; "ILIST"; "NNI"; "BOOLEAN"; "STEP"}*/ +/*"LPARSPT" -> {"UPOLYC"; "PI"; "LSAGG-"; "STAGG-"; "OUTFORM"; "ELAGG-"}*/ + "MDAGG" [color="#4488FF",href="bookvol10.2.pdf#nameddest=MDAGG"] "MDAGG" -> "DIOPS" /*"MDAGG" -> {"BGAGG"; "HOAGG"; "AGG"; "TYPE"; "SETCAT"; "BASTYPE"}*/ @@ -17038,6 +17060,21 @@ ${MID}/PRJALGPK.nrlib/code.o: ${MID}/PRJALGPK.spad | ${INTERPSYS} >${TMP}/trace ; \ fi ) @ +<>= + +LPARSPTDEPS = PRSPCAT LOCPOWC SETCATD PLACESC PLPKCRV PFORP + +${MID}/LPARSPT.nrlib/code.o: ${MID}/LPARSPT.spad + @echo P3 making ${MID}/LPARSPT.nrlib/code.o from ${MID}/LPARSPT.spad + @ (cd ${MID} ; \ + if [ -z "${NOISE}" ] ; then \ + echo -e ")lib ${LPARSPTDEPS} \n )co LPARSPT.spad" \ + | ${INTERPSYS} ; \ + else \ + echo -e ")lib ${LPARSPTDEPS} \n )co AFALGRES.spad" \ + | ${INTERPSYS} >${TMP}/trace ; \ + fi ) +@ \section{Broken Files} These files are Aldor files @@ -17829,6 +17866,7 @@ SPADHELP=\ ${HELP}/LinearSystemFromPowerSeriesPackage.help \ ${HELP}/List.help \ ${HELP}/LinesOpPack.help \ + ${HELP}/LocalParametrizationOfSimplePointPackage.help \ ${HELP}/LocalPowerSeriesCategory.help \ ${HELP}/LyndonWord.help \ ${HELP}/Magma.help \ @@ -18034,6 +18072,7 @@ REGRESS= \ LinearSystemFromPowerSeriesPackage.regress \ List.regress \ LinesOpPack.regress \ + LocalParametrizationOfSimplePointPackage.regress \ LocalPowerSeriesCategory.regress \ LyndonWord.regress \ Magma.regress \ @@ -19136,8 +19175,23 @@ ${HELP}/LinesOpPack.help: ${BOOKS}/bookvol10.4.pamphlet >${INPUT}/LinesOpPack.input @echo "LinesOpPack (LOP)" >>${HELPFILE} +${HELP}/LocalParametrizationOfSimplePointPackage.help: \ + ${BOOKS}/bookvol10.4.pamphlet + @echo 7577 create LocalParametrizationOfSimplePointPackage.help from \ + ${BOOKS}/bookvol10.4.pamphlet + @${TANGLE} -R"LocalParametrizationOfSimplePointPackage.help" \ + ${BOOKS}/bookvol10.4.pamphlet \ + >${HELP}/LocalParametrizationOfSimplePointPackage.help + @cp ${HELP}/LocalParametrizationOfSimplePointPackage.help \ + ${HELP}/LPARSPT.help + @${TANGLE} -R"LocalParametrizationOfSimplePointPackage.input" \ + ${BOOKS}/bookvol10.4.pamphlet \ + >${INPUT}/LocalParametrizationOfSimplePointPackage.input + @echo "LocalParametrizationOfSimplePointPackage (LPARSPT)" \ + >>${HELPFILE} + ${HELP}/LocalPowerSeriesCategory.help: ${BOOKS}/bookvol10.2.pamphlet - @echo 7577 create LocalPowerSeriesCategory.help from \ + @echo 7578 create LocalPowerSeriesCategory.help from \ ${BOOKS}/bookvol10.2.pamphlet @${TANGLE} -R"LocalPowerSeriesCategory.help" \ ${BOOKS}/bookvol10.2.pamphlet \ diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index b8fd504..9519814 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2787,5 +2787,7 @@ books/bookvol10.4 add AffineAlgebraicSetComputeWithResultant
books/bookvol10.4 AffineAlgebraicSetComputeWithGroebnerBasis.eps
20100523.01.tpd.patch books/bookvol10.4 add ProjectiveAlgebraicSetPackage
+20100523.02.tpd.patch +books/bookvol10.4 add LocalParametrizationOfSimplePointPackage