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GRTensorIII package for Maple
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Cannot calc CM after assume(S>0); #25

Open grtensor opened 6 years ago

grtensor commented 6 years ago

assume(S > 0); grcalc(CM); Error, (in grtensor:-grcalc) cannot convert index difference:, up, nearList[1]

Something to do with the use of an object S?

ctzounis commented 4 years ago

I get similar problems when I try:

grdef(u1o{a}:=[rho(z,V),-f(z,V),0,0]): grdef(u2o{a}:=[-f(z,V),-tau(z,V),0,0]): grdef(u3o{a}:=[0,0,p(z,V),0]): grdef(u4o{a}:=[0,0,0,p(z,V)]): grdef(Tso{a b}:=u1o{b}*kdelta{a $V}+u2o{b}*kdelta{a $z}+u3o{b}*kdelta{a $theta}+u4o{b}*kdelta{a $phi}): grcalc(Tso(dn,dn)):

OUTCOME

Components assigned for metric: NEWevaporatingbh1 Created definition for u1o(dn) Components assigned for metric: NEWevaporatingbh1 Created definition for u2o(dn) Components assigned for metric: NEWevaporatingbh1 Created definition for u3o(dn) Components assigned for metric: NEWevaporatingbh1 Created definition for u4o(dn) Warning = cannot convert index difference: Created definition for Tso(dn,dn) Error, (in grtensor:-grcalc) cannot convert index difference:, dn, nearList[1]

Do you know what is the problem?

grtensor commented 4 years ago

Thanks for reporting this.

Are you able to provide the worksheet that produces the issue? What was the assume() ? (I tried a quick example with Reisnner-Nordstrom and your definitions but could not reproduce. See attached.)

Thanks,

Peter

On Wed, Sep 18, 2019 at 4:44 PM ctzounis notifications@github.com wrote:

I get similar problems when I try:

grdef(u1o{a}:=[rho(z,V),-f(z,V),0,0]): grdef(u2o{a}:=[-f(z,V),-tau(z,V),0,0]): grdef(u3o{a}:=[0,0,p(z,V),0]): grdef(u4o{a}:=[0,0,0,p(z,V)]): grdef(Tso{a b}:=u1o{b}kdelta{a $V}+u2o{b}kdelta{a $z}+u3o{b}kdelta{a $theta}+u4o{b}kdelta{a $phi}): grcalc(Tso(dn,dn)):

OUTCOME

Components assigned for metric: NEWevaporatingbh1 Created definition for u1o(dn) Components assigned for metric: NEWevaporatingbh1 Created definition for u2o(dn) Components assigned for metric: NEWevaporatingbh1 Created definition for u3o(dn) Components assigned for metric: NEWevaporatingbh1 Created definition for u4o(dn) Warning = cannot convert index difference: Created definition for Tso(dn,dn) Error, (in grtensor:-grcalc) cannot convert index difference:, dn, nearList[1]

Do you know what is the problem?

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ctzounis commented 4 years ago

This is the code:

restart:

alpha:=f0(16Pi*beta):

k3:=0:

k6:=-(5/6)k5+xi-20f0+5*k3:

k7:=xi+5k3-5k5(1/6)-20f0-k6;

ms:=(-3alphaV)^(1/3): ms2:=(-3alphaV)^(1/3)+4alpha(1/z-ln(z)-1)/(-3alphaV)^(1/3): B:=1-ln(z)(64betaPif0/ms2^2)+g1(z)/(ms2^2); MBH:=ms2(1+f1(z)/ms2^2): r:=2ms2/z: rV:=expand(diff(r,V)); rZ:=expand(diff(r,z)); F1(z,V):=(B^2(1-2MBH/r)-2BrV): H1(z,V):=BrZ: W1(z,V):=r^2: ps:=beta/ms^4: fw(z):=f0z^2/(1-z);

con:=xi: p2(x):=x^4(k4+k5x+k6x^2)+k3x^3+k7*x^7:

pw(z):=z^4(k4+k5z+k6z^2)+k3z^3+k7z^7: G(z):=expand(int((2/x^3-3/x^2)p2(x),x=z..1)): T(z):=conz^6; H(z):=con/10(1-z^5);

G(z):=expand(int((2/x^3-3/x^2)*p2(x),x=z..1));

beta:=1/(2^(13)3^25*Pi^2):

rhow(z):=((-fw(z)+2pw(z)+z^2/(1-z)(H(z)+G(z))-T(z))): rhotest:=z^2(f0/(1-z)(1-30z^4+28z^5)+xi/2z^4-k3/2(z^2+z^3-14z^4)+k4z^2+k5/6(8z^3-7z^4)): simplify(rhow(z)-rhotest); tauw(z):=(-z^2/(1-z)(H(z)+G(z))+fw(z)); factorxi:=simplify(coeff(rhow(z),xi)); factorf0:=(simplify(coeff(rhow(z),f0))); factork3:=factor(simplify(coeff(rhow(z),k3))); factork4:=simplify(coeff(rhow(z),k4)); factork5:=simplify(coeff(rhow(z),k5));

factorxi1:=simplify(coeff(tauw(z),xi)); factorf01:=(simplify(coeff(tauw(z),f0))); factork31:=factor(simplify(coeff(tauw(z),k3))); factork41:=simplify(coeff(tauw(z),k4)); factork51:=simplify(coeff(tauw(z),k5)); rhotest:=expand(-z^2/(60(1-z))(60f0+60z^3k4-60z^2k4+75z^4k5-80z^3k5+84k6z^5-90z^4k6+30z^2k3-6xi-54xiz^5+6k6+5k5-30k3+60xiz^4)): tautest:=z^2/(60(1-z))(-6xi+6xiz^5-36k6z^5+30z^4k6-45z^4k5+40z^3k5-60z^3k4+60z^2k4-90z^2k3+120zk3+6k6+5k5-30k3+60f0): simplify(rhow(z)-rhotest); simplify(tauw(z)-tautest); f(z,V):=psfw(z): p(z,V):=pspw(z): tau(z,V):=pstauw(z): rho(z,V):=psrhow(z):

f1(z):= simplify((1/15)(-224Pibetaz^4k6+144Pibetaz^4xi+24z^3Pibetak6-300z^3Pibetak5-24z^3Pibetaxi+40z^2Pibetak5-480z^2Pibetak4+48z^2Pibetak6-48z^2Pibetaxi-480ln(z-1)f0Pibetaz+30ln(z-1)alphaz-30alphaln(z)z+1440f0Pibetaln(z)z-240ln(z)Pibetak3z+40ln(z)Pibetak5z-48ln(z)Pibetaxiz+48ln(z)Pibetak6z+30alpha-1440f0Pibeta+240Pibetak3-40Pibetak5+48Pibetaxi-48Pibetak6+15_C2*z)/z);

g1(z):= simplify((-(1/15)(30-30z)alpha/(z-1)-(1/15)(480z-480)Pif0beta/(z-1))ln(z-1)+(-(1/15)(-30+30z)alpha/(z-1)+(-(1/15)(48z-48)Pixi/(z-1)-(1/15)(-48z+48)Pik6/(z-1)-(1/15)(-40z+40)Pik5/(z-1)-(1/15)(-240+240z)Pik3/(z-1)-(1/15)(480z-480)Pif0/(z-1))beta)ln(z)+2alpha/(z-1)+(-(1/15)(8z^3-96z+24z^2+64z^4)Pixi/(z-1)-(1/15)(-8z^3-64z^4+96z-24z^2)Pik6/(z-1)-(1/15)(-60z^3-20z^2+80z)Pik5/(z-1)-32f0Pi/(z-1))beta-(1/15)(-15z+15)*_C1/(z-1));

subs(z=0,f1(z));

subs(z=0,g1(z));

simplify(tau(z,V)-ps*tauw(z));

with(grtensor); spacetime(NEWevaporatingbh1,coord=[V,z,theta,phi],ds=-F1(z,V)d[V]^2+2H1(z,V)d[V]d[z]+W1(z,V)sin(theta)^2d[phi]^2+W1(z,V)d[theta]^2); grdef(u1o{a}:=[rho(z,V),-f(z,V),0,0]): grdef(u2o{a}:=[-f(z,V),-tau(z,V),0,0]): grdef(u3o{a}:=[0,0,p(z,V),0]): grdef(u4o{a}:=[0,0,0,p(z,V)]): grdef(`Tso{a b}:=u1o{b}kdelta{a $V}+u2o{b}kdelta{a $z}+u3o{b}kdelta{a $theta}+u4o{b}*kdelta{a $phi}`): grcalc(Tso(dn,dn)): grcalc(G(dn,dn)):

After grcalc(Tso(dn,dn)):, I get the following output:

Components assigned for metric: NEWevaporatingbh1 Created definition for u1o(dn) Components assigned for metric: NEWevaporatingbh1 Created definition for u2o(dn) Components assigned for metric: NEWevaporatingbh1 Created definition for u3o(dn) Components assigned for metric: NEWevaporatingbh1 Created definition for u4o(dn) Warning = cannot convert index difference: Created definition for Tso(dn,dn) Error, (in grtensor:-grcalc) cannot convert index difference:, dn, nearList[1]

Is this more helpful?

grtensor commented 4 years ago

Thanks.

I can now reproduce. It is something to do with the use of kdelta. I'll see if I can find the bug this week.

Peter

On Fri, Sep 20, 2019 at 6:45 PM ctzounis notifications@github.com wrote:

This is the code:

restart:

alpha:=f0(16Pi*beta):

k3:=0:

k6:=-(5/6)k5+xi-20f0+5

k3: #k7:=xi+5k3-5k5(1/6)-20 f0-k6; ms:=(-3alpha V)^(1/3): ms2:=(-3alphaV)^(1/3)+4alpha(1/z-ln(z)-1)/(-3alpha V)^(1/3): B:=1-ln(z)(64betaPif0/ms2^2)+g1(z)/(ms2^2); MBH:=ms2(1+f1(z)/ms2^2): r:=2

ms2/z: rV:=expand(diff(r,V)); rZ:=expand(diff(r,z)); F1(z,V):=(B^2(1-2 MBH/r)-2B rV): H1(z,V):=BrZ: W1(z,V):=r^2: ps:=beta/ms^4: fw(z):=f0*z^2/(1-z);

con:=xi: p2(x):=x^4(k4+k5x+k6x^2)+k3x^3+k7*x^7:

pw(z):=z^4(k4+k5z+k6z^2)+k3z^3+k7z^7: G(z):=expand(int((2/x^3-3/x^2) p2(x),x=z..1)): T(z):=conz^6; H(z):=con/10(1-z^5);

G(z):=expand(int((2/x^3-3/x^2) p2(x),x=z..1)); #beta:=1/(2^(13)3^25Pi^2): rhow(z):=((-fw(z)+2pw(z)+z^2/(1-z)(H(z)+G(z))-T(z))): rhotest:=z^2(f0/(1-z)(1-30z^4+28z^5)+xi/2z^4-k3/2(z^2+z^3-14 z^4)+k4z^2+k5/6(8z^3-7z^4)): simplify(rhow(z)-rhotest); tauw(z):=(-z^2/(1-z)(H(z)+G(z))+fw(z)); factorxi:=simplify(coeff(rhow(z),xi)); factorf0:=(simplify(coeff(rhow(z),f0))); factork3:=factor(simplify(coeff(rhow(z),k3))); factork4:=simplify(coeff(rhow(z),k4)); factork5:=simplify(coeff(rhow(z),k5));

factorxi1:=simplify(coeff(tauw(z),xi)); factorf01:=(simplify(coeff(tauw(z),f0))); factork31:=factor(simplify(coeff(tauw(z),k3))); factork41:=simplify(coeff(tauw(z),k4)); factork51:=simplify(coeff(tauw(z),k5)); rhotest:=expand(-z^2/(60(1-z))(60f0+60z^3k4-60z^2k4+75z^4k5-80 z^3k5+84k6z^5-90z^4k6+30z^2k3-6xi-54xiz^5+6k6+5k5-30k3+60 xiz^4)): tautest:=z^2/(60(1-z))(-6xi+6xiz^5-36k6z^5+30z^4k6-45z^4k5+40 z^3k5-60z^3k4+60z^2k4-90z^2k3+120zk3+6k6+5k5-30k3+60f0): simplify(rhow(z)-rhotest); simplify(tauw(z)-tautest); f(z,V):=ps fw(z): p(z,V):=pspw(z): tau(z,V):=ps tauw(z): rho(z,V):=psrhow(z):

f1(z):= simplify((1/15)(-224Pibetaz^4k6+144Pibetaz^4xi+24z^3

Pibetak6-300z^3Pibetak5-24z^3Pibetaxi+40z^2Pibetak5-480z^2 Pibetak4+48z^2Pibetak6-48z^2Pibetaxi-480ln(z-1)f0Pibeta z+30ln(z-1)alphaz-30alphaln(z)z+1440f0Pibetaln(z)z-240ln(z)Pi betak3z+40ln(z)Pibetak5z-48ln(z)Pibetaxiz+48ln(z)Pibetak6 z+30alpha-1440f0Pibeta+240Pibetak3-40Pibetak5+48Pibetaxi-48 Pibetak6+15_C2 z)/z); #g1(z):= simplify((-(1/15)(30-30z)alpha/(z-1)-(1/15)(480z-480) Pif0beta/(z-1))ln(z-1)+(-(1/15)(-30+30z)alpha/(z-1)+(-(1/15)(48 z-48)Pixi/(z-1)-(1/15)(-48z+48)Pik6/(z-1)-(1/15)(-40 z+40)Pik5/(z-1)-(1/15)(-240+240z)Pik3/(z-1)-(1/15)(480 z-480)Pif0/(z-1))beta)ln(z)+2alpha/(z-1)+(-(1/15)(8z^3-96z+24z^2+64 z^4)Pixi/(z-1)-(1/15)(-8z^3-64z^4+96z-24z^2)Pik6/(z-1)-(1/15) (-60z^3-20z^2+80z)Pik5/(z-1)-32f0Pi/(z-1))beta-(1/15)(-15z+15)

*C1/(z-1)); #subs(z=0,f1(z)); #subs(z=0,g1(z));

simplify(tau(z,V)-pstauw(z)); grtw();

spacetime(NEWevaporatingbh1,coord=[V,z,theta,phi],ds=-F1(z,V)d[V]^2+2 H1(z,V)d[V]d[z]+W1(z,V)sin(theta)^2d[phi]^2+W1(z,V)d[theta]^2); grdef(u1o{a}:=[rho(z,V),-f(z,V),0,0]): grdef(u2o{a}:=[-f(z,V),-tau(z,V),0,0]): grdef(u3o{a}:=[0,0,p(z,V),0]): grdef(u4o{a}:=[0,0,0,p(z,V)]): grdef(Tso{a b}:=u1o{b}kdelta{a $V}+u2o{b}kdelta{a $z}+u3o{b}kdelta{a $theta}+u4o{b}*kdelta{a $phi}): grcalc(Tso(dn,dn)): grcalc(G(dn,dn)):

After grcalc(Tso(dn,dn)):, I get the following output:

Components assigned for metric: NEWevaporatingbh1 Created definition for u1o(dn) Components assigned for metric: NEWevaporatingbh1 Created definition for u2o(dn) Components assigned for metric: NEWevaporatingbh1 Created definition for u3o(dn) Components assigned for metric: NEWevaporatingbh1 Created definition for u4o(dn) Warning = cannot convert index difference: Created definition for Tso(dn,dn) Error, (in grtensor:-grcalc) cannot convert index difference:, dn, nearList[1]

Is this more helpful?

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grtensor commented 4 years ago

Not sure why yet, but if you change your coordinate V to lower case v, the error is avoided.

Peter

On Sun, Sep 22, 2019 at 10:28 AM Peter Musgrave grtensor3@gmail.com wrote:

Thanks.

I can now reproduce. It is something to do with the use of kdelta. I'll see if I can find the bug this week.

Peter

On Fri, Sep 20, 2019 at 6:45 PM ctzounis notifications@github.com wrote:

This is the code:

restart:

alpha:=f0(16Pi*beta):

k3:=0:

k6:=-(5/6)k5+xi-20f0+5

k3: #k7:=xi+5k3-5k5(1/6)-20 f0-k6; ms:=(-3alpha V)^(1/3): ms2:=(-3alphaV)^(1/3)+4alpha(1/z-ln(z)-1)/(-3alpha V)^(1/3): B:=1-ln(z)(64betaPif0/ms2^2)+g1(z)/(ms2^2); MBH:=ms2(1+f1(z)/ms2^2): r:=2

ms2/z: rV:=expand(diff(r,V)); rZ:=expand(diff(r,z)); F1(z,V):=(B^2(1-2 MBH/r)-2B rV): H1(z,V):=BrZ: W1(z,V):=r^2: ps:=beta/ms^4: fw(z):=f0*z^2/(1-z);

con:=xi: p2(x):=x^4(k4+k5x+k6x^2)+k3x^3+k7*x^7:

pw(z):=z^4(k4+k5z+k6z^2)+k3z^3+k7z^7: G(z):=expand(int((2/x^3-3/x^2) p2(x),x=z..1)): T(z):=conz^6; H(z):=con/10(1-z^5);

G(z):=expand(int((2/x^3-3/x^2) p2(x),x=z..1)); #beta:=1/(2^(13)3^25Pi^2): rhow(z):=((-fw(z)+2pw(z)+z^2/(1-z)(H(z)+G(z))-T(z))): rhotest:=z^2(f0/(1-z)(1-30z^4+28z^5)+xi/2z^4-k3/2(z^2+z^3-14 z^4)+k4z^2+k5/6(8z^3-7z^4)): simplify(rhow(z)-rhotest); tauw(z):=(-z^2/(1-z)(H(z)+G(z))+fw(z)); factorxi:=simplify(coeff(rhow(z),xi)); factorf0:=(simplify(coeff(rhow(z),f0))); factork3:=factor(simplify(coeff(rhow(z),k3))); factork4:=simplify(coeff(rhow(z),k4)); factork5:=simplify(coeff(rhow(z),k5));

factorxi1:=simplify(coeff(tauw(z),xi)); factorf01:=(simplify(coeff(tauw(z),f0))); factork31:=factor(simplify(coeff(tauw(z),k3))); factork41:=simplify(coeff(tauw(z),k4)); factork51:=simplify(coeff(tauw(z),k5)); rhotest:=expand(-z^2/(60(1-z))(60f0+60z^3k4-60z^2k4+75z^4k5-80 z^3k5+84k6z^5-90z^4k6+30z^2k3-6xi-54xiz^5+6k6+5k5-30k3+60 xiz^4)): tautest:=z^2/(60(1-z))(-6xi+6xiz^5-36k6z^5+30z^4k6-45z^4k5+40 z^3k5-60z^3k4+60z^2k4-90z^2k3+120zk3+6k6+5k5-30k3+60f0): simplify(rhow(z)-rhotest); simplify(tauw(z)-tautest); f(z,V):=ps fw(z): p(z,V):=pspw(z): tau(z,V):=ps tauw(z): rho(z,V):=psrhow(z):

f1(z):= simplify((1/15)(-224Pibetaz^4k6+144Pibetaz^4xi+24z^3

Pibetak6-300z^3Pibetak5-24z^3Pibetaxi+40z^2Pibetak5-480 z^2Pibetak4+48z^2Pibetak6-48z^2Pibetaxi-480ln(z-1)f0Pi betaz+30ln(z-1)alphaz-30alphaln(z)z+1440f0Pibetaln(z)z-240ln(z) Pibetak3z+40ln(z)Pibetak5z-48ln(z)Pibetaxiz+48ln(z)Pibetak6 z+30alpha-1440f0Pibeta+240Pibetak3-40Pibetak5+48Pibetaxi-48 Pibetak6+15_C2 z)/z); #g1(z):= simplify((-(1/15)(30-30z)alpha/(z-1)-(1/15)(480z-480) Pif0beta/(z-1))ln(z-1)+(-(1/15)(-30+30z)alpha/(z-1)+(-(1/15)(48 z-48)Pixi/(z-1)-(1/15)(-48z+48)Pik6/(z-1)-(1/15)(-40 z+40)Pik5/(z-1)-(1/15)(-240+240z)Pik3/(z-1)-(1/15)(480 z-480)Pif0/(z-1))beta)ln(z)+2alpha/(z-1)+(-(1/15)(8z^3-96z+24z^2+64 z^4)Pixi/(z-1)-(1/15)(-8z^3-64z^4+96z-24z^2)Pik6/(z-1)-(1/15) (-60z^3-20z^2+80z)Pik5/(z-1)-32f0Pi/(z-1))beta-(1/15)(-15 z+15)

*C1/(z-1)); #subs(z=0,f1(z)); #subs(z=0,g1(z));

simplify(tau(z,V)-pstauw(z)); grtw();

spacetime(NEWevaporatingbh1,coord=[V,z,theta,phi],ds=-F1(z,V)d[V]^2+2 H1(z,V)d[V]d[z]+W1(z,V)sin(theta)^2d[phi]^2+W1(z,V)d[theta]^2); grdef(u1o{a}:=[rho(z,V),-f(z,V),0,0]): grdef(u2o{a}:=[-f(z,V),-tau(z,V),0,0]): grdef(u3o{a}:=[0,0,p(z,V),0]): grdef(u4o{a}:=[0,0,0,p(z,V)]): grdef(Tso{a b}:=u1o{b}kdelta{a $V}+u2o{b}kdelta{a $z}+u3o{b}kdelta{a $theta}+u4o{b}*kdelta{a $phi}): grcalc(Tso(dn,dn)): grcalc(G(dn,dn)):

After grcalc(Tso(dn,dn)):, I get the following output:

Components assigned for metric: NEWevaporatingbh1 Created definition for u1o(dn) Components assigned for metric: NEWevaporatingbh1 Created definition for u2o(dn) Components assigned for metric: NEWevaporatingbh1 Created definition for u3o(dn) Components assigned for metric: NEWevaporatingbh1 Created definition for u4o(dn) Warning = cannot convert index difference: Created definition for Tso(dn,dn) Error, (in grtensor:-grcalc) cannot convert index difference:, dn, nearList[1]

Is this more helpful?

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ctzounis commented 4 years ago

I will try it. Thanks.