MaplePrimes Questions

I wish to substitute only the base of the ifactor expression like the following

lst := [24300, 18907875, 151200, 147000]

[24300, 18907875, 151200, 147000]

(1)

map(ifactor, lst)

[``(2)^2*``(3)^5*``(5)^2, ``(3)^2*``(5)^3*``(7)^5, ``(2)^5*``(3)^3*``(5)^2*``(7), ``(2)^3*``(3)*``(5)^3*``(7)^2]

(2)

subs(2 = x, %)

[``(x)^x*``(3)^5*``(5)^x, ``(3)^x*``(5)^3*``(7)^5, ``(x)^5*``(3)^3*``(5)^x*``(7), ``(x)^3*``(3)*``(5)^3*``(7)^x]

(3)

I wish my results to be

[x^2*3^5*5^2, 3^2*5^3*7^5, 7*x^5*3^3*5^2, 3*x^3*5^3*7^2]

[6075*x^2, 18907875, 4725*x^5, 18375*x^3]

(4)

such that

subs(x = 2, %)

[24300, 18907875, 151200, 147000]

(5)

evalb(% = lst)

true

(6)

NULL

Download SubsExample.mw

If there a way to do that? I understand that there is a command ifactors which gives me more control, but the form of the result is rather inconvenient. I hope there is a more direct way to do the aforementioned operation.

How can I draw Steiner trees of hypercubes in graph theory? 

With the following steps

S1: Open Help pressing F1

S2: enter `if in the search field

S3: click a topic in the result list

S4: search within the topic with find/replace (Crtl f) the term `if 

I get plenty of results where I cannot find the search term in the help topic. Why is that?

Is help ignoring the left single quotes ` ?

I don't think so: I get usefull results for `` and `i, which in the later case also lists the topic "ifelse" that contains `if in the textbody.

So, why does advanced searching with the exact phrase "`if" not list the "ifelse" topic?

Realted question:

Why does the search term "(* " not list the relevant help topic help(comment)?

Somehow related in the context of getting more specific results:

https://www.mapleprimes.com/questions/234462-Searching-The-Help-System-Why-Are-There-No-Hits-For-Solve

Hi,

Can anyone help me with the following technique?

solutions:

 

Are there any restrictions regarding path and filename length in Maple?

I am experiencing problems working with a file on a server, path and file length is 207 characters.

Using Maple-18 on Window 11...

I have a set of curves in a Maple 'vector.' I want to plot them all on the same figure, but if call 'display' with the vector it makes separate plots for each one. I have to all it with each plot individual to get them on the same plot:

lc is a 'vector' of curves (I use 'vector' because I want to append and that doesn't work for 'list')

display(lc) -- plots a separate plot for each element of lc

display(lc[1], lc[2], lc[3],...) puts them all on one plot as needed, but as there will be a large numbe of curvesr it's extremely tedious.

It is a Huygens principle based simulation of diffraction.

restart

estart; with(Physics); with(LinearAlgebra); with(VectorCalculus); with(Optimization); with(Statistics); with(ArrayTools); with(plots); with(plottools); with(Threads); with(MmaTranslator[Mma]), with(StringTools); with(CodeGeneration); with(ImageTools); with(ImageTools:-Draw); VectorCalculus:-`*`(Setup(mathematicalnotation = true), Setup(coordinatesystems = cartesian))

estart

 

[annulus, arc, arrow, circle, cone, cuboid, curve, cutin, cutout, cylinder, disk, dodecahedron, ellipse, ellipticArc, exportplot, extrude, getdata, hemisphere, hexahedron, homothety, hyperbola, icosahedron, importplot, line, octahedron, parallelepiped, pieslice, point, polygon, prism, project, rectangle, reflect, rotate, scale, sector, semitorus, sphere, stellate, tetrahedron, torus, transform, translate]

 

`Default differentiation variables for d_, D_ and dAlembertian are:`*{X = (x, y, z, t)}

 

`Systems of spacetime Coordinates are:`*{X = (x, y, z, t)}

(1)

NULL

NULL

 

radius := 1.0

1.0

(2)

NULL

NULL

``

NULL

alpha := sin((1/4)*Pi)

(1/2)*2^(1/2)

(3)

step := .2

.2

(4)

radius := 100.0

100.0

(5)

l1 := line([0, 0], [100, 100])

CURVES([[0., 0.], [100., 100.]])

(6)

loAng := 0.

0.

(7)

hiAng := (1/2)*Pi

(1/2)*Pi

(8)

c1 := arc([0, 0.], radius, loAng .. Pi, color = "red")

c2 := arc([step, 0.], -alpha*step+radius, loAng .. hiAng, color = "blue")

c3 := arc([2*step, 0.], -2*alpha*step+radius, loAng .. Pi, color = "purple")

c4 := arc([3*step, 0.], -3*alpha*step+radius, loAng .. Pi, color = "black")

plots[display](l1, c1, c2, c3, c4, view = [0. .. radius, 0 .. radius])

 

`cir≔arc`([x, 0.], radius-step, loAng .. hiAng, i, color = "red")

`cir≔arc`([x, 0.], 99.8, 0. .. (1/2)*Pi, i, color = "red")

(9)

``

xLimitWall := 500.0; nScatter := 20; step := xLimitWall/(nScatter+1); x := 0.; for i from 0 to nScatter do x := x+step; cir := arc([x, 0.], radius-step, 0 .. Pi, color = "red"); if i = 0 then lc := Vector([cir]) else i; cir; Append(lc, cir) end if end do; lc

xLimitWall := 500.0

 

nScatter := 20

 

step := 23.80952381

 

x := 0.

 

x := 23.80952381

 

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

 

x := 47.61904762

 

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

 

x := 71.42857143

 

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

 

x := 95.23809524

 

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

 

x := 119.0476190

 

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

 

x := 142.8571428

 

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

 

x := 166.6666666

 

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

 

x := 190.4761904

 

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

 

x := 214.2857142

 

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

 

x := 238.0952380

 

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

 

x := 261.9047618

 

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

 

x := 285.7142856

 

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

 

x := 309.5238094

 

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

 

x := 333.3333332

 

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

 

x := 357.1428570

 

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

 

x := 380.9523808

 

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

 

x := 404.7619046

 

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

 

x := 428.5714284

 

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

 

x := 452.3809522

 

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

 

x := 476.1904760

 

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

 

x := 499.9999998

 

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

 

Vector[column](%id = 4400555778)

(10)

lc[1]

CURVES(Matrix(%id = 4400554242), COLOUR(RGB, 1.00000000, 0., 0.))

(11)

lc(2)

``

lc

lc[1]

``

Download JFKWEdgeDifractionDirection.mwJFKWEdgeDifractionDirection.mwen.

Maple 2022.2

> restart
> expr = x^4-10*x^2+1
> plot(expr)

produces an error message:
com.maplesoft.maplets.ComponentAccessException: not a valid plot structure

plot(expr, x) works Ok.

Tom Dean

Hi, I'm trying to figure out, how to differentiate the following expression:

I also don't get how to properly index (indefinite) sum terms... Grateful for any advice!

How to fix the error?

How are they (tanh(a+b) , tanh(a-b)) defined in Maple?

Ger.mw

How to find the series.I'm getting this error.Please help to solve this.

AF.mw

I want to express my two variable function f using Taylor expansion. But no success yet.

Why Taylor series can not estimate my function in desired interval [-1<x,y<1]?

restart

with(Student[MultivariateCalculus]):

 

f := -5023626067733175609651265492842895195168362165*xx^5*yy^9*(1/5575186299632655785383929568162090376495104)+2207379816207475241162406248223006569040862935*xx^5*yy^8*(1/2787593149816327892691964784081045188247552)+5795161625895678368156852916105373987594511979*xx^6*(1/22300745198530623141535718272648361505980416)-539977758872163289054492124375185771143918033*xx^6*yy*(1/696898287454081973172991196020261297061888)+782685832362921584689673760969891945953777553*xx^6*yy^2*(1/5575186299632655785383929568162090376495104)+749877940244270735637721966049124917356845885*xx^6*yy^3*(1/174224571863520493293247799005065324265472)+14159347676475748959036290080103848146860867025*xx^6*yy^4*(1/11150372599265311570767859136324180752990208)-2937701213452088192123555543440803264914467299*xx^6*yy^5*(1/348449143727040986586495598010130648530944)-23673134207774883972271882396704370580007933039*xx^6*yy^6*(1/5575186299632655785383929568162090376495104)-62755544772437504320590342390381422715234113715/89202980794122492566142873090593446023921664+35696532930567486560276536615522532283474689213*yy*(1/2787593149816327892691964784081045188247552)+43423414494451507811145033075147441881593811799*yy^2*(1/22300745198530623141535718272648361505980416)+1173296429365947392287371443632107462978009165*xx^6*yy^7*(1/174224571863520493293247799005065324265472)-56566850002827011453690682806041619180254985625*yy^3*(1/696898287454081973172991196020261297061888)+57447439083834576362467553225131370438848237035*xx^6*yy^8*(1/22300745198530623141535718272648361505980416)-1277356081222180962342283013232991241852904465*xx^6*yy^9*(1/696898287454081973172991196020261297061888)-29946355461657315300256240552185966952551471*xx^7*(1/1393796574908163946345982392040522594123776)+998213736763384913910074759047227544847506773*xx^7*yy*(1/11150372599265311570767859136324180752990208)-2038600361316622246653155899145012259420048867785*yy^4*(1/44601490397061246283071436545296723011960832)+10578825782023300845453772557509072093336001*xx^7*yy^2*(1/43556142965880123323311949751266331066368)-4303517165264733669855129139552505045324631645*xx^7*yy^3*(1/11150372599265311570767859136324180752990208)-652299342907430898149182084981866414949696905*xx^7*yy^4*(1/696898287454081973172991196020261297061888)+11170081785792631086653879206603595320491089331*xx^7*yy^5*(1/11150372599265311570767859136324180752990208)+116540829629507365267125159526451609264014215*xx^7*yy^6*(1/87112285931760246646623899502532662132736)+211134394987302797546644924545169826774270265159*yy^5*(1/1393796574908163946345982392040522594123776)-14785537121406447202257499440081382142298519099*xx^7*yy^7*(1/11150372599265311570767859136324180752990208)+1970986683407627074325019523003479974617451789943*yy^6*(1/22300745198530623141535718272648361505980416)-868641325364973493898126340263842300348545855*xx^7*yy^8*(1/1393796574908163946345982392040522594123776)+216255546256559295251079313253452049445763455*xx^7*yy^9*(1/348449143727040986586495598010130648530944)-4089215965643055747590786827106386135115380275*xx^8*(1/89202980794122492566142873090593446023921664)+1869246621670048362557342074310025153518449965*xx^8*yy*(1/2787593149816327892691964784081045188247552)+18712604797880071317805036942199122521197359575*xx^8*yy^2*(1/22300745198530623141535718272648361505980416)-3479476522267890993628796487849129439635143625*xx^8*yy^3*(1/696898287454081973172991196020261297061888)-77131555128675321096947207038878222843991869993*yy^7*(1/696898287454081973172991196020261297061888)-206512033439850904054937113093163624192322042825*xx^8*yy^4*(1/44601490397061246283071436545296723011960832)+15350689937843699961175740256400109996121380375*xx^8*yy^5*(1/1393796574908163946345982392040522594123776)+157001869330425518481531763580902779395436599415*xx^8*yy^6*(1/22300745198530623141535718272648361505980416)-6686861200533386632065997818427854246215113305*xx^8*yy^7*(1/696898287454081973172991196020261297061888)-3917684154726736823398471536296978037714283086195*yy^8*(1/89202980794122492566142873090593446023921664)-285743684916570536194588196441080828723328178675*xx^8*yy^8*(1/89202980794122492566142873090593446023921664)+8094790880015327525694605814920739418439287725*xx^8*yy^9*(1/2787593149816327892691964784081045188247552)+30423874459994412977383604476886160940746185*xx^9*(1/5575186299632655785383929568162090376495104)-1197236208181378637639504269592639035279087665*xx^9*yy*(1/44601490397061246283071436545296723011960832)-72716798311978341010558827315982986191821905*xx^9*yy^2*(1/696898287454081973172991196020261297061888)+5138909461003175489938484170634052266819688725*xx^9*yy^3*(1/44601490397061246283071436545296723011960832)+1206817075246069632318716986669541278160772775*xx^9*yy^4*(1/2787593149816327892691964784081045188247552)-12993287722661922638788467553649639108437064835*xx^9*yy^5*(1/44601490397061246283071436545296723011960832)-431284328058774504067793959976795724976545555*xx^9*yy^6*(1/696898287454081973172991196020261297061888)+17639360745426635511855086638766468926126459875*xx^9*yy^7*(1/44601490397061246283071436545296723011960832)-2146702909675882809503682033933399905335826325*xx^9*yy^9*(1/11150372599265311570767859136324180752990208)+1587967252519403636411870604735180043125989625*xx^9*yy^8*(1/5575186299632655785383929568162090376495104)+76828297887427851822683521168415270943435162685*yy^9*(1/2787593149816327892691964784081045188247552)+220816865194317615868568855814620996552449073*xx*(1/5575186299632655785383929568162090376495104)-9205355621994819342146712860571987786619361601*xx*yy*(1/44601490397061246283071436545296723011960832)-104255809907916433055923335622932126645726549*xx*yy^2*(1/696898287454081973172991196020261297061888)+27484692689867334306687311759874973819976026005*xx*yy^3*(1/44601490397061246283071436545296723011960832)+1583056855557692418384969876461998197073089695*xx*yy^4*(1/2787593149816327892691964784081045188247552)-36304948749180317956941914133403396762716230691*xx*yy^5*(1/44601490397061246283071436545296723011960832)-590212436135125327923049635849260481403670583*xx*yy^6*(1/696898287454081973172991196020261297061888)+27046038795224386955728969793334632924015008227*xx*yy^7*(1/44601490397061246283071436545296723011960832)+2168816628024980374461014350770096009019357665*xx*yy^8*(1/5575186299632655785383929568162090376495104)-2255097230860381206152749351617455809672044745*xx*yy^9*(1/11150372599265311570767859136324180752990208)+35122173917479363738100862234581108137514304171*xx^2*(1/22300745198530623141535718272648361505980416)-17449701902039745490242163912540688306429882361*xx^2*yy*(1/696898287454081973172991196020261297061888)-11540959773500599403794316292492996114189538863*xx^2*yy^2*(1/5575186299632655785383929568162090376495104)+27287439738914744607616926917914225474665410565*xx^2*yy^3*(1/174224571863520493293247799005065324265472)+929769947314964740179937673332890647768037984465*xx^2*yy^4*(1/11150372599265311570767859136324180752990208)-100809382380090436397261413740272360141145204891*xx^2*yy^5*(1/348449143727040986586495598010130648530944)-930314746723434588666177195703059675161177190255*xx^2*yy^6*(1/5575186299632655785383929568162090376495104)+36390552938954376406834468187448925576623439893*xx^2*yy^7*(1/174224571863520493293247799005065324265472)+1872760743346397986120124413411813119412045269675*xx^2*yy^8*(1/22300745198530623141535718272648361505980416)-35643509355104072817665294345590475660747146425*xx^2*yy^9*(1/696898287454081973172991196020261297061888)-125283292999146417157156696376640452081866835*xx^3*(1/1393796574908163946345982392040522594123776)+5011420945327438626354964312196465908094234685*xx^3*yy*(1/11150372599265311570767859136324180752990208)+29341459645317546529685572705520876577051855*xx^3*yy^2*(1/87112285931760246646623899502532662132736)-15637727799880882327290754576104647826715168925*xx^3*yy^3*(1/11150372599265311570767859136324180752990208)-851688199122087410134053760306093104684621525*xx^3*yy^4*(1/696898287454081973172991196020261297061888)+23458516464006675395891679247259419002768896835*xx^3*yy^5*(1/11150372599265311570767859136324180752990208)+39584968580329795728950940517214770307434335*xx^3*yy^6*(1/21778071482940061661655974875633165533184)-20361225581568567923686744589522827658576624955*xx^3*yy^7*(1/11150372599265311570767859136324180752990208)-1174244552874873223035231031480900497934023075*xx^3*yy^8*(1/1393796574908163946345982392040522594123776)+941109349474535911451616661821106567867537125*xx^3*yy^9*(1/1393796574908163946345982392040522594123776)-48412290717709997717153300332089796247538326265*xx^4*(1/44601490397061246283071436545296723011960832)+17196469545705046799299985950707233685621881055*xx^4*yy*(1/1393796574908163946345982392040522594123776)-9551461763890264957289963973620923748598225435*xx^4*yy^2*(1/11150372599265311570767859136324180752990208)-26051472095770585704126329008135447818638784275*xx^4*yy^3*(1/348449143727040986586495598010130648530944)-765302392604646459013613426858243443467023490875*xx^4*yy^4*(1/22300745198530623141535718272648361505980416)+94251624724512021502035994822030873708141367565*xx^4*yy^5*(1/696898287454081973172991196020261297061888)+843981485493394825713526892530506348990296828805*xx^4*yy^6*(1/11150372599265311570767859136324180752990208)-33218490572036542393092937176469859040906121155*xx^4*yy^7*(1/348449143727040986586495598010130648530944)-1758702445038817232726176779731884586549332868025*xx^4*yy^8*(1/44601490397061246283071436545296723011960832)+31380186488931551370058361496245928395816772575*xx^4*yy^9*(1/1393796574908163946345982392040522594123776)+184838927094446995029201369223921105703104647*xx^5*(1/2787593149816327892691964784081045188247552)-6817973449093402642853212701104432585928821163*xx^5*yy*(1/22300745198530623141535718272648361505980416)-113510140727511300460098712979462156361337425*xx^5*yy^2*(1/348449143727040986586495598010130648530944)+23570688854853763073042723518782612790921757535*xx^5*yy^3*(1/22300745198530623141535718272648361505980416)+1613038118657167505912389296857854524947676825*xx^5*yy^4*(1/1393796574908163946345982392040522594123776)-44608078263668464626393951292252447406629869273*xx^5*yy^5*(1/22300745198530623141535718272648361505980416)-588774433706353379897742534304221654039246663*xx^5*yy^6*(1/348449143727040986586495598010130648530944)+47950825635610780986659544491454706340397108297*xx^5*yy^7*(1/22300745198530623141535718272648361505980416):

g := .5*(1+tanh(f)):

plot3d(g, xx = -1 .. 1, yy = -1 .. 1, color = red, style = surface)

 

 

h := Student:-MultivariateCalculus:-TaylorApproximation(g, [xx, yy] = [0, 0], 35):

plot3d(h, xx = -1 .. 1, yy = -1 .. 1, color = red, style = surface)

 

 

Download taylorProblem.mw

How I can solve a PDE on two regions with matching conditions at the common boundary?  

T1.mw

In Maple 2023 I haven't been able to sign in to the Maple Cloud.
In Maple 2022 there was no problem. In fact in my Maple 2022.2 I'm actually signed in right now.

I need this to get updates to the Physics updates. 
The toolbar in 2023.2 has a grayed out icon saying "Sign in". Nothing happens if I click on it.

PS. I'm also signed in right now to Maple 2021.2. So the problem couldn't be that I cannot be logged in to more than one Maple release.

[Moderator: long pasted output deleted - OP has provided file in reply]

According to the documentation of MmaTranslator:-Mma:-PolynomialReduce, this command yields . However, 

restart;
MmaTranslator:-Mma:-PolynomialReduce(x**2+y**2,{x-y,y+a});
 = 
                       [         2    2]
                       [[0, 0], x  + y ]

In[1]:= PolynomialReduce[x^2+y^2,{x-y,y+a}](*Mathematica*)

Out[1]= {{x + y, -2 a + 2 y}, 2 a^2}

In SymPy and in MuPAD: 

The output of both is the same as that of Mma; only the result given by Maple is inconsistent with Mathematica's. 

The example above is so simple that the desired result can be found simply by hand. Here is a larger example: 
Given two polynomials .txt and .txt, as well as a list of polynomials .txt, I would like to evaluate 

# Suppose that one has downloaded these three files. 
poly1, poly2 := fscanf("poly1.txt", "%a")[], fscanf("poly2.txt", "%a")[]:
pList := MmaTranslator:-Mma:-ReadList("pList.txt"):
MmaTranslator:-Mma:-PolynomialReduce((a - poly1)*(a - poly2), pList);

 But its result is just “[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ]”, while when a=0 it should be “[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 1, 1, 1, 1, 0, 0, 0, 1, 2, 1, 0, 2, 2, 3, 1, 1, 1, 2, 1, 0, 0, 0, 1, 1, 2, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0], 0]”.
So why does  return a distinct value?

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