diff --git a/books/bookvol10.4.pamphlet b/books/bookvol10.4.pamphlet index 95f1b04..315d833 100644 --- a/books/bookvol10.4.pamphlet +++ b/books/bookvol10.4.pamphlet @@ -138948,7 +138948,7 @@ StreamTaylorSeriesOperations(A): Exports == Implementation where ++ first order non-linear differential equation described by u of the ++ form \spad{[[b<0,0>,b<0,1>,...],[b<1,0>,b<1,1>,.],...]}. ++ the differential equation has the form - ++ \spad{y' = sum(i=0 to infinity,j=0 to infinity,b*(x**i)*(y**j))}. + ++ \spad{y'=sum(i=0 to infinity,j=0 to infinity,b*(x**i)*(y**j))}. powern : (RN,ST A) -> ST A ++ powern(r,f) raises power series f to the power r. if A has Field then @@ -138973,18 +138973,18 @@ StreamTaylorSeriesOperations(A): Exports == Implementation where x + y == delay empty? y => x empty? x => y - eq?(x,rst x) => map(frst x + #1,y) - eq?(y,rst y) => map(frst y + #1,x) + eq?(x,rst x) => map(z +-> frst x+z, y) + eq?(y,rst y) => map(z +-> frst y+z, x) concat(frst x + frst y,rst x + rst y) x - y == delay empty? y => x empty? x => -y - eq?(x,rst x) => map(frst x - #1,y) - eq?(y,rst y) => map(#1 - frst y,x) + eq?(x,rst x) => map(z +-> frst x-z, y) + eq?(y,rst y) => map(z +-> z-frst y, x) concat(frst x - frst y,rst x - rst y) - -y == map(_-#1,y) + -y == map(z +-> -z, y) (x:ST A) * (y:ST A) == delay empty? y => zro() @@ -138993,11 +138993,11 @@ StreamTaylorSeriesOperations(A): Exports == Implementation where (s:A) * (x:ST A) == zero? s => zro() - map(s * #1,x) + map(z +-> s*z, x) (x:ST A) * (s:A) == zero? s => zro() - map(#1 * s,x) + map(z +-> z*s, x) iDiv: (ST A,ST A,A) -> ST A iDiv(x,y,ry0) == delay @@ -139015,7 +139015,7 @@ StreamTaylorSeriesOperations(A): Exports == Implementation where return "failed" leave "first entry in y is non-zero" (ry0 := recip frst y) case "failed" => "failed" - empty? rst y => map(#1 * (ry0 :: A),x) + empty? rst y => map(z +-> z*(ry0 :: A), x) iDiv(x,y,ry0 :: A) (x:ST A) / (y:ST A) == delay @@ -139023,7 +139023,7 @@ StreamTaylorSeriesOperations(A): Exports == Implementation where empty? x => empty() (ry0 := recip frst y) case "failed" => error "/: second argument is not invertible" - empty? rst y => map(#1 * (ry0 :: A),x) + empty? rst y => map(z +-> z*(ry0::A),x) iDiv(x,y,ry0 :: A) recip x == @@ -139054,10 +139054,10 @@ StreamTaylorSeriesOperations(A): Exports == Implementation where --% some streams of integers nnintegers: NNI -> ST NNI - nnintegers zz == generate(#1 + 1,zz) - integers z == generate(#1 + 1,z) - oddintegers z == generate(#1 + 2,z) - int s == generate(#1 + 1,s) + nnintegers zz == generate(y +-> y+1, zz) + integers z == generate(y +-> y+1, z) + oddintegers z == generate(y +-> y+2, z) + int s == generate(y +-> y+1, s) --% derivatives @@ -139082,7 +139082,8 @@ StreamTaylorSeriesOperations(A): Exports == Implementation where --% evaluations and compositions - eval(x,at) == scan(0,#1 + #2,mapmult(x,generate(at * #1,1)))$SP2(A,A) + eval(x,at) == + scan(0,(y,z) +-> y+z,mapmult(x,generate(y +-> at*y,1)))$SP2(A,A) compose(x,y) == delay empty? y => concat(frst x,zro()) @@ -139095,7 +139096,7 @@ StreamTaylorSeriesOperations(A): Exports == Implementation where lagrangere:(ST A,ST A) -> ST A lagrangere(x,c) == delay(concat(0,compose(x,c))) - lagrange x == YS(lagrangere(x,#1)) + lagrange x == YS(y +-> lagrangere(x,y)) revert x == empty? x => error "revert should start 0,1,..." @@ -139155,7 +139156,7 @@ StreamTaylorSeriesOperations(A): Exports == Implementation where error "generalLambert: both integer arguments must be positive" empty? st => zro() zero? frst st => - concat(0,addiag(map(rptg3(a,d,#1,#2),_ + concat(0,addiag(map((x,y) +-> rptg3(a,d,x,y), integers 1,rst st)$SP3(I,A,ST A))) error "generalLambert: constant coefficient should be zero" @@ -139186,7 +139187,7 @@ StreamTaylorSeriesOperations(A): Exports == Implementation where comps(ststa,x) == delay$(ST ST A) empty? ststa => empty()$(ST ST A) empty? x => cssa(frst ststa,empty()$(ST ST A)) - cssa(frst ststa,mapsa((rst x) * #1,comps(rst ststa,x))) + cssa(frst ststa,mapsa(y +-> (rst x)*y,comps(rst ststa,x))) if A has Algebra RN then integre: (ST A,I) -> ST A @@ -139202,12 +139203,12 @@ StreamTaylorSeriesOperations(A): Exports == Implementation where nldere:(ST ST A,ST A) -> ST A nldere(lslsa,c) == lazyIntegrate(0,addiag(comps(lslsa,c))) - nlde lslsa == YS(nldere(lslsa,#1)) + nlde lslsa == YS(y +-> nldere(lslsa,y)) RATPOWERS : Boolean := A has "**": (A,RN) -> A smult: (RN,ST A) -> ST A - smult(rn,x) == map(rn * #1,x) + smult(rn,x) == map(y +-> rn*y, x) powerrn:(RN,ST A,ST A) -> ST A powerrn(rn,x,c) == delay concat(1,integ(smult(rn + 1,c * deriv x)) - rst x * c) @@ -139226,15 +139227,15 @@ StreamTaylorSeriesOperations(A): Exports == Implementation where error "** rational power of coefficient undefined" -- This error message is misleading, isn't it? see sups.spad/cRationalPower power := --- one? co => YS(powerrn(rn,x,#1)) - (co = 1) => YS(powerrn(rn,x,#1)) +-- one? co => YS(y +-> powerrn(rn,x,y)) + (co = 1) => YS(y +-> powerrn(rn,x,y)) (denom rn) = 1 => not negative?(num := numer rn) => -- It seems that this cannot happen, but I don't know why - (co**num::NNI) * YS(powerrn(rn,(invCo :: A) * x,#1)) - (invCo :: A)**((-num)::NNI) * YS(powerrn(rn,(invCo :: A) * x,#1)) + (co**num::NNI) * YS(y +-> powerrn(rn,(invCo :: A) * x, y)) + (invCo::A)**((-num)::NNI) * YS(y +-> powerrn(rn,(invCo :: A)*x, y)) - RATPOWERS => co**rn * YS(powerrn(rn,(invCo :: A) * x,#1)) + RATPOWERS => co**rn * YS(y +-> powerrn(rn,(invCo :: A)*x, y)) error "** rational power of coefficient undefined" if A has Field then @@ -139255,7 +139256,7 @@ StreamTaylorSeriesOperations(A): Exports == Implementation where empty? x => zro() frst x^=1 => error "**:constant coefficient should be 1" concat(frst x,finteg((s+1)*(c*deriv x))-rst x * c) - power(s,x) == YS(powerre(s,x,#1)) + power(s,x) == YS(y +-> powerre(s,x,y)) @ <>= diff --git a/changelog b/changelog index 3538ca1..1c0b9c6 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,5 @@ +20090621 tpd src/axiom-website/patches.html 20090621.06.tpd.patch +20090621 tpd books/bookvol10.4 STTAYLOR +-> conversion 20090621 tpd src/axiom-website/patches.html 20090621.05.tpd.patch 20090621 tpd books/bookvol10.4 STINPROD +-> conversion 20090621 tpd src/axiom-website/patches.html 20090621.04.tpd.patch diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 148b200..19891bc 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -1627,5 +1627,7 @@ bookvol10.4 SFRGCD +-> conversion
bookvol10.4 STREAM3 +-> conversion
20090621.05.tpd.patch bookvol10.4 STINPROD +-> conversion
+20090621.06.tpd.patch +bookvol10.4 STTAYLOR +-> conversion