I have to show that (!P.!Q+R)(!Q+P.!R) => !Q by simplifying it using De Morgan's Laws.
Here is what I did but I'm not sure it's right.
(!P.!Q + R)(!Q + P.!R) => !Q
(!P + !Q + R)(!Q + P.!R)
!P.!Q + !P.P.!R + !Q.!Q + !Q.P.!R + R.!Q + R.P.!R
!P.!Q + 0 + !Q + !Q.P.!Q + R.!Q + 0
!P.!Q + !Q + !Q(1 + P.!R + R)
!P.!Q + !Q + !Q
!Q + !P.!Q
!Q(1 + !P)
!Q
Hope that's clear enough.
Related
I am trying to solve a non-linear equation system with maxima.
I use wxmaxima (17.05.0). The non-linear system is rather long and I am deeply sorry for posting the hole problem, but otherwise I do not think my problem will be clear.
I would like to solve these equations for eleven unkowns (K2 to K11) When I run this after some time the error message "No more room for LISP objects" occurs.
I have no glue how I can give it more cpu or to avoid the error.
I need the symbolic solutions for further calculations.
debugmode(true);
gcd : subres;
eq1:mBA*(K10*RABm10 + K11*RABm11 + K12*RABm12 + K7*RABm7 + K8*RABm8 + K9*RABm9)*
(M1 + K10*M10*RAm10 + K11*M11*RAm11 + K12*M12*RAm12 + K2*M2*RAm2 +
K3*M3*RAm3 + K4*M4*RAm4 + K5*M5*RAm5 + K6*M6*RAm6 + K7*M7*RAm7 +
K8*M8*RAm8 + K9*M9*RAm9)*
(1 + K2*RBm2 + K3*RBm3 + K4*RBm4 + K5*RBm5 + K6*RBm6) +
mAB*(K10*RABm10 + K11*RABm11 + K12*RABm12 + K7*RABm7 + K8*RABm8 +
K9*RABm9)*(1 + K2*RAm2 + K3*RAm3 + K4*RAm4 + K5*RAm5 + K6*RAm6)*
(M1 + K10*M10*RBm10 + K11*M11*RBm11 + K12*M12*RBm12 + K2*M2*RBm2 +
K3*M3*RBm3 + K4*M4*RBm4 + K5*M5*RBm5 + K6*M6*RBm6 + K7*M7*RBm7 +
K8*M8*RBm8 + K9*M9*RBm9) =
mBA*(K10*RABm10 + K11*RABm11 + K12*RABm12 + K7*RABm7 + K8*RABm8 +
K9*RABm9)*(M1 + K10*M10*RAm10 + K11*M11*RAm11 + K12*M12*RAm12 +
K2*M2*RAm2 + K3*M3*RAm3 + K4*M4*RAm4 + K5*M5*RAm5 + K6*M6*RAm6 +
K7*M7*RAm7 + K8*M8*RAm8 + K9*M9*RAm9)*
(K10*RBm10 + K11*RBm11 + K12*RBm12 + K7*RBm7 + K8*RBm8 + K9*RBm9) +
mAB*(K10*RABm10 + K11*RABm11 + K12*RABm12 + K7*RABm7 + K8*RABm8 +
K9*RABm9)*(K10*RAm10 + K11*RAm11 + K12*RAm12 + K7*RAm7 + K8*RAm8 +
K9*RAm9)*(M1 + K10*M10*RBm10 + K11*M11*RBm11 + K12*M12*RBm12 +
K2*M2*RBm2 + K3*M3*RBm3 + K4*M4*RBm4 + K5*M5*RBm5 + K6*M6*RBm6 +
K7*M7*RBm7 + K8*M8*RBm8 + K9*M9*RBm9)$
eq2:mCA*(K10*RACm10 + K11*RACm11 + K12*RACm12 + K7*RACm7 + K8*RACm8 + K9*RACm9)*
(M1 + K10*M10*RAm10 + K11*M11*RAm11 + K12*M12*RAm12 + K2*M2*RAm2 +
K3*M3*RAm3 + K4*M4*RAm4 + K5*M5*RAm5 + K6*M6*RAm6 + K7*M7*RAm7 +
K8*M8*RAm8 + K9*M9*RAm9)*
(1 + K2*RCm2 + K3*RCm3 + K4*RCm4 + K5*RCm5 + K6*RCm6) +
mAC*(K10*RACm10 + K11*RACm11 + K12*RACm12 + K7*RACm7 + K8*RACm8 +
K9*RACm9)*(1 + K2*RAm2 + K3*RAm3 + K4*RAm4 + K5*RAm5 + K6*RAm6)*
(M1 + K10*M10*RCm10 + K11*M11*RCm11 + K12*M12*RCm12 + K2*M2*RCm2 +
K3*M3*RCm3 + K4*M4*RCm4 + K5*M5*RCm5 + K6*M6*RCm6 + K7*M7*RCm7 +
K8*M8*RCm8 + K9*M9*RCm9) =
mCA*(K10*RACm10 + K11*RACm11 + K12*RACm12 + K7*RACm7 + K8*RACm8 +
K9*RACm9)*(M1 + K10*M10*RAm10 + K11*M11*RAm11 + K12*M12*RAm12 +
K2*M2*RAm2 + K3*M3*RAm3 + K4*M4*RAm4 + K5*M5*RAm5 + K6*M6*RAm6 +
K7*M7*RAm7 + K8*M8*RAm8 + K9*M9*RAm9)*
(K10*RCm10 + K11*RCm11 + K12*RCm12 + K7*RCm7 + K8*RCm8 + K9*RCm9) +
mAC*(K10*RACm10 + K11*RACm11 + K12*RACm12 + K7*RACm7 + K8*RACm8 +
K9*RACm9)*(K10*RAm10 + K11*RAm11 + K12*RAm12 + K7*RAm7 + K8*RAm8 +
K9*RAm9)*(M1 + K10*M10*RCm10 + K11*M11*RCm11 + K12*M12*RCm12 +
K2*M2*RCm2 + K3*M3*RCm3 + K4*M4*RCm4 + K5*M5*RCm5 + K6*M6*RCm6 +
K7*M7*RCm7 + K8*M8*RCm8 + K9*M9*RCm9)$
eq3:mDA*(K10*RADm10 + K11*RADm11 + K12*RADm12 + K7*RADm7 + K8*RADm8 + K9*RADm9)*
(M1 + K10*M10*RAm10 + K11*M11*RAm11 + K12*M12*RAm12 + K2*M2*RAm2 +
K3*M3*RAm3 + K4*M4*RAm4 + K5*M5*RAm5 + K6*M6*RAm6 + K7*M7*RAm7 +
K8*M8*RAm8 + K9*M9*RAm9)*
(1 + K2*RDm2 + K3*RDm3 + K4*RDm4 + K5*RDm5 + K6*RDm6) +
mAD*(K10*RADm10 + K11*RADm11 + K12*RADm12 + K7*RADm7 + K8*RADm8 +
K9*RADm9)*(1 + K2*RAm2 + K3*RAm3 + K4*RAm4 + K5*RAm5 + K6*RAm6)*
(M1 + K10*M10*RDm10 + K11*M11*RDm11 + K12*M12*RDm12 + K2*M2*RDm2 +
K3*M3*RDm3 + K4*M4*RDm4 + K5*M5*RDm5 + K6*M6*RDm6 + K7*M7*RDm7 +
K8*M8*RDm8 + K9*M9*RDm9) =
mDA*(K10*RADm10 + K11*RADm11 + K12*RADm12 + K7*RADm7 + K8*RADm8 +
K9*RADm9)*(M1 + K10*M10*RAm10 + K11*M11*RAm11 + K12*M12*RAm12 +
K2*M2*RAm2 + K3*M3*RAm3 + K4*M4*RAm4 + K5*M5*RAm5 + K6*M6*RAm6 +
K7*M7*RAm7 + K8*M8*RAm8 + K9*M9*RAm9)*
(K10*RDm10 + K11*RDm11 + K12*RDm12 + K7*RDm7 + K8*RDm8 + K9*RDm9) +
mAD*(K10*RADm10 + K11*RADm11 + K12*RADm12 + K7*RADm7 + K8*RADm8 +
K9*RADm9)*(K10*RAm10 + K11*RAm11 + K12*RAm12 + K7*RAm7 + K8*RAm8 +
K9*RAm9)*(M1 + K10*M10*RDm10 + K11*M11*RDm11 + K12*M12*RDm12 +
K2*M2*RDm2 + K3*M3*RDm3 + K4*M4*RDm4 + K5*M5*RDm5 + K6*M6*RDm6 +
K7*M7*RDm7 + K8*M8*RDm8 + K9*M9*RDm9)$
eq4:mEA*(K10*RAEm10 + K11*RAEm11 + K12*RAEm12 + K7*RAEm7 + K8*RAEm8 + K9*RAEm9)*
(M1 + K10*M10*RAm10 + K11*M11*RAm11 + K12*M12*RAm12 + K2*M2*RAm2 +
K3*M3*RAm3 + K4*M4*RAm4 + K5*M5*RAm5 + K6*M6*RAm6 + K7*M7*RAm7 +
K8*M8*RAm8 + K9*M9*RAm9)*
(1 + K2*REm2 + K3*REm3 + K4*REm4 + K5*REm5 + K6*REm6) +
mAE*(K10*RAEm10 + K11*RAEm11 + K12*RAEm12 + K7*RAEm7 + K8*RAEm8 +
K9*RAEm9)*(1 + K2*RAm2 + K3*RAm3 + K4*RAm4 + K5*RAm5 + K6*RAm6)*
(M1 + K10*M10*REm10 + K11*M11*REm11 + K12*M12*REm12 + K2*M2*REm2 +
K3*M3*REm3 + K4*M4*REm4 + K5*M5*REm5 + K6*M6*REm6 + K7*M7*REm7 +
K8*M8*REm8 + K9*M9*REm9) =
mEA*(K10*RAEm10 + K11*RAEm11 + K12*RAEm12 + K7*RAEm7 + K8*RAEm8 +
K9*RAEm9)*(M1 + K10*M10*RAm10 + K11*M11*RAm11 + K12*M12*RAm12 +
K2*M2*RAm2 + K3*M3*RAm3 + K4*M4*RAm4 + K5*M5*RAm5 + K6*M6*RAm6 +
K7*M7*RAm7 + K8*M8*RAm8 + K9*M9*RAm9)*
(K10*REm10 + K11*REm11 + K12*REm12 + K7*REm7 + K8*REm8 + K9*REm9) +
mAE*(K10*RAEm10 + K11*RAEm11 + K12*RAEm12 + K7*RAEm7 + K8*RAEm8 +
K9*RAEm9)*(K10*RAm10 + K11*RAm11 + K12*RAm12 + K7*RAm7 + K8*RAm8 +
K9*RAm9)*(M1 + K10*M10*REm10 + K11*M11*REm11 + K12*M12*REm12 +
K2*M2*REm2 + K3*M3*REm3 + K4*M4*REm4 + K5*M5*REm5 + K6*M6*REm6 +
K7*M7*REm7 + K8*M8*REm8 + K9*M9*REm9)$
eq5:mFA*(K10*RAFm10 + K11*RAFm11 + K12*RAFm12 + K7*RAFm7 + K8*RAFm8 + K9*RAFm9)*
(M1 + K10*M10*RAm10 + K11*M11*RAm11 + K12*M12*RAm12 + K2*M2*RAm2 +
K3*M3*RAm3 + K4*M4*RAm4 + K5*M5*RAm5 + K6*M6*RAm6 + K7*M7*RAm7 +
K8*M8*RAm8 + K9*M9*RAm9)*
(1 + K2*RFm2 + K3*RFm3 + K4*RFm4 + K5*RFm5 + K6*RFm6) +
mAF*(K10*RAFm10 + K11*RAFm11 + K12*RAFm12 + K7*RAFm7 + K8*RAFm8 +
K9*RAFm9)*(1 + K2*RAm2 + K3*RAm3 + K4*RAm4 + K5*RAm5 + K6*RAm6)*
(M1 + K10*M10*RFm10 + K11*M11*RFm11 + K12*M12*RFm12 + K2*M2*RFm2 +
K3*M3*RFm3 + K4*M4*RFm4 + K5*M5*RFm5 + K6*M6*RFm6 + K7*M7*RFm7 +
K8*M8*RFm8 + K9*M9*RFm9) =
mFA*(K10*RAFm10 + K11*RAFm11 + K12*RAFm12 + K7*RAFm7 + K8*RAFm8 +
K9*RAFm9)*(M1 + K10*M10*RAm10 + K11*M11*RAm11 + K12*M12*RAm12 +
K2*M2*RAm2 + K3*M3*RAm3 + K4*M4*RAm4 + K5*M5*RAm5 + K6*M6*RAm6 +
K7*M7*RAm7 + K8*M8*RAm8 + K9*M9*RAm9)*
(K10*RFm10 + K11*RFm11 + K12*RFm12 + K7*RFm7 + K8*RFm8 + K9*RFm9) +
mAF*(K10*RAFm10 + K11*RAFm11 + K12*RAFm12 + K7*RAFm7 + K8*RAFm8 +
K9*RAFm9)*(K10*RAm10 + K11*RAm11 + K12*RAm12 + K7*RAm7 + K8*RAm8 +
K9*RAm9)*(M1 + K10*M10*RFm10 + K11*M11*RFm11 + K12*M12*RFm12 +
K2*M2*RFm2 + K3*M3*RFm3 + K4*M4*RFm4 + K5*M5*RFm5 + K6*M6*RFm6 +
K7*M7*RFm7 + K8*M8*RFm8 + K9*M9*RFm9)$
eq6:mGA*(K10*RAGm10 + K11*RAGm11 + K12*RAGm12 + K7*RAGm7 + K8*RAGm8 + K9*RAGm9)*
(M1 + K10*M10*RAm10 + K11*M11*RAm11 + K12*M12*RAm12 + K2*M2*RAm2 +
K3*M3*RAm3 + K4*M4*RAm4 + K5*M5*RAm5 + K6*M6*RAm6 + K7*M7*RAm7 +
K8*M8*RAm8 + K9*M9*RAm9)*
(1 + K2*RGm2 + K3*RGm3 + K4*RGm4 + K5*RGm5 + K6*RGm6) +
mAG*(K10*RAGm10 + K11*RAGm11 + K12*RAGm12 + K7*RAGm7 + K8*RAGm8 +
K9*RAGm9)*(1 + K2*RAm2 + K3*RAm3 + K4*RAm4 + K5*RAm5 + K6*RAm6)*
(M1 + K10*M10*RGm10 + K11*M11*RGm11 + K12*M12*RGm12 + K2*M2*RGm2 +
K3*M3*RGm3 + K4*M4*RGm4 + K5*M5*RGm5 + K6*M6*RGm6 + K7*M7*RGm7 +
K8*M8*RGm8 + K9*M9*RGm9) =
mGA*(K10*RAGm10 + K11*RAGm11 + K12*RAGm12 + K7*RAGm7 + K8*RAGm8 +
K9*RAGm9)*(M1 + K10*M10*RAm10 + K11*M11*RAm11 + K12*M12*RAm12 +
K2*M2*RAm2 + K3*M3*RAm3 + K4*M4*RAm4 + K5*M5*RAm5 + K6*M6*RAm6 +
K7*M7*RAm7 + K8*M8*RAm8 + K9*M9*RAm9)*
(K10*RGm10 + K11*RGm11 + K12*RGm12 + K7*RGm7 + K8*RGm8 + K9*RGm9) +
mAG*(K10*RAGm10 + K11*RAGm11 + K12*RAGm12 + K7*RAGm7 + K8*RAGm8 +
K9*RAGm9)*(K10*RAm10 + K11*RAm11 + K12*RAm12 + K7*RAm7 + K8*RAm8 +
K9*RAm9)*(M1 + K10*M10*RGm10 + K11*M11*RGm11 + K12*M12*RGm12 +
K2*M2*RGm2 + K3*M3*RGm3 + K4*M4*RGm4 + K5*M5*RGm5 + K6*M6*RGm6 +
K7*M7*RGm7 + K8*M8*RGm8 + K9*M9*RGm9)$
eq7:mHA*(K10*RAHm10 + K11*RAHm11 + K12*RAHm12 + K7*RAHm7 + K8*RAHm8 + K9*RAHm9)*
(M1 + K10*M10*RAm10 + K11*M11*RAm11 + K12*M12*RAm12 + K2*M2*RAm2 +
K3*M3*RAm3 + K4*M4*RAm4 + K5*M5*RAm5 + K6*M6*RAm6 + K7*M7*RAm7 +
K8*M8*RAm8 + K9*M9*RAm9)*
(1 + K2*RHm2 + K3*RHm3 + K4*RHm4 + K5*RHm5 + K6*RHm6) +
mAH*(K10*RAHm10 + K11*RAHm11 + K12*RAHm12 + K7*RAHm7 + K8*RAHm8 +
K9*RAHm9)*(1 + K2*RAm2 + K3*RAm3 + K4*RAm4 + K5*RAm5 + K6*RAm6)*
(M1 + K10*M10*RHm10 + K11*M11*RHm11 + K12*M12*RHm12 + K2*M2*RHm2 +
K3*M3*RHm3 + K4*M4*RHm4 + K5*M5*RHm5 + K6*M6*RHm6 + K7*M7*RHm7 +
K8*M8*RHm8 + K9*M9*RHm9) =
mHA*(K10*RAHm10 + K11*RAHm11 + K12*RAHm12 + K7*RAHm7 + K8*RAHm8 +
K9*RAHm9)*(M1 + K10*M10*RAm10 + K11*M11*RAm11 + K12*M12*RAm12 +
K2*M2*RAm2 + K3*M3*RAm3 + K4*M4*RAm4 + K5*M5*RAm5 + K6*M6*RAm6 +
K7*M7*RAm7 + K8*M8*RAm8 + K9*M9*RAm9)*
(K10*RHm10 + K11*RHm11 + K12*RHm12 + K7*RHm7 + K8*RHm8 + K9*RHm9) +
mAH*(K10*RAHm10 + K11*RAHm11 + K12*RAHm12 + K7*RAHm7 + K8*RAHm8 +
K9*RAHm9)*(K10*RAm10 + K11*RAm11 + K12*RAm12 + K7*RAm7 + K8*RAm8 +
K9*RAm9)*(M1 + K10*M10*RHm10 + K11*M11*RHm11 + K12*M12*RHm12 +
K2*M2*RHm2 + K3*M3*RHm3 + K4*M4*RHm4 + K5*M5*RHm5 + K6*M6*RHm6 +
K7*M7*RHm7 + K8*M8*RHm8 + K9*M9*RHm9)$
eq8:mIA*(K10*RAIm10 + K11*RAIm11 + K12*RAIm12 + K7*RAIm7 + K8*RAIm8 + K9*RAIm9)*
(M1 + K10*M10*RAm10 + K11*M11*RAm11 + K12*M12*RAm12 + K2*M2*RAm2 +
K3*M3*RAm3 + K4*M4*RAm4 + K5*M5*RAm5 + K6*M6*RAm6 + K7*M7*RAm7 +
K8*M8*RAm8 + K9*M9*RAm9)*
(1 + K2*RIm2 + K3*RIm3 + K4*RIm4 + K5*RIm5 + K6*RIm6) +
mAI*(K10*RAIm10 + K11*RAIm11 + K12*RAIm12 + K7*RAIm7 + K8*RAIm8 +
K9*RAIm9)*(1 + K2*RAm2 + K3*RAm3 + K4*RAm4 + K5*RAm5 + K6*RAm6)*
(M1 + K10*M10*RIm10 + K11*M11*RIm11 + K12*M12*RIm12 + K2*M2*RIm2 +
K3*M3*RIm3 + K4*M4*RIm4 + K5*M5*RIm5 + K6*M6*RIm6 + K7*M7*RIm7 +
K8*M8*RIm8 + K9*M9*RIm9) =
mIA*(K10*RAIm10 + K11*RAIm11 + K12*RAIm12 + K7*RAIm7 + K8*RAIm8 +
K9*RAIm9)*(M1 + K10*M10*RAm10 + K11*M11*RAm11 + K12*M12*RAm12 +
K2*M2*RAm2 + K3*M3*RAm3 + K4*M4*RAm4 + K5*M5*RAm5 + K6*M6*RAm6 +
K7*M7*RAm7 + K8*M8*RAm8 + K9*M9*RAm9)*
(K10*RIm10 + K11*RIm11 + K12*RIm12 + K7*RIm7 + K8*RIm8 + K9*RIm9) +
mAI*(K10*RAIm10 + K11*RAIm11 + K12*RAIm12 + K7*RAIm7 + K8*RAIm8 +
K9*RAIm9)*(K10*RAm10 + K11*RAm11 + K12*RAm12 + K7*RAm7 + K8*RAm8 +
K9*RAm9)*(M1 + K10*M10*RIm10 + K11*M11*RIm11 + K12*M12*RIm12 +
K2*M2*RIm2 + K3*M3*RIm3 + K4*M4*RIm4 + K5*M5*RIm5 + K6*M6*RIm6 +
K7*M7*RIm7 + K8*M8*RIm8 + K9*M9*RIm9)$
eq9:mJA*(K10*RAJm10 + K11*RAJm11 + K12*RAJm12 + K7*RAJm7 + K8*RAJm8 + K9*RAJm9)*
(M1 + K10*M10*RAm10 + K11*M11*RAm11 + K12*M12*RAm12 + K2*M2*RAm2 +
K3*M3*RAm3 + K4*M4*RAm4 + K5*M5*RAm5 + K6*M6*RAm6 + K7*M7*RAm7 +
K8*M8*RAm8 + K9*M9*RAm9)*
(1 + K2*RJm2 + K3*RJm3 + K4*RJm4 + K5*RJm5 + K6*RJm6) +
mAJ*(K10*RAJm10 + K11*RAJm11 + K12*RAJm12 + K7*RAJm7 + K8*RAJm8 +
K9*RAJm9)*(1 + K2*RAm2 + K3*RAm3 + K4*RAm4 + K5*RAm5 + K6*RAm6)*
(M1 + K10*M10*RJm10 + K11*M11*RJm11 + K12*M12*RJm12 + K2*M2*RJm2 +
K3*M3*RJm3 + K4*M4*RJm4 + K5*M5*RJm5 + K6*M6*RJm6 + K7*M7*RJm7 +
K8*M8*RJm8 + K9*M9*RJm9) =
mJA*(K10*RAJm10 + K11*RAJm11 + K12*RAJm12 + K7*RAJm7 + K8*RAJm8 +
K9*RAJm9)*(M1 + K10*M10*RAm10 + K11*M11*RAm11 + K12*M12*RAm12 +
K2*M2*RAm2 + K3*M3*RAm3 + K4*M4*RAm4 + K5*M5*RAm5 + K6*M6*RAm6 +
K7*M7*RAm7 + K8*M8*RAm8 + K9*M9*RAm9)*
(K10*RJm10 + K11*RJm11 + K12*RJm12 + K7*RJm7 + K8*RJm8 + K9*RJm9) +
mAJ*(K10*RAJm10 + K11*RAJm11 + K12*RAJm12 + K7*RAJm7 + K8*RAJm8 +
K9*RAJm9)*(K10*RAm10 + K11*RAm11 + K12*RAm12 + K7*RAm7 + K8*RAm8 +
K9*RAm9)*(M1 + K10*M10*RJm10 + K11*M11*RJm11 + K12*M12*RJm12 +
K2*M2*RJm2 + K3*M3*RJm3 + K4*M4*RJm4 + K5*M5*RJm5 + K6*M6*RJm6 +
K7*M7*RJm7 + K8*M8*RJm8 + K9*M9*RJm9)$
eq10:mKA*(K10*RAKm10 + K11*RAKm11 + K12*RAKm12 + K7*RAKm7 + K8*RAKm8 + K9*RAKm9)*
(M1 + K10*M10*RAm10 + K11*M11*RAm11 + K12*M12*RAm12 + K2*M2*RAm2 +
K3*M3*RAm3 + K4*M4*RAm4 + K5*M5*RAm5 + K6*M6*RAm6 + K7*M7*RAm7 +
K8*M8*RAm8 + K9*M9*RAm9)*
(1 + K2*RKm2 + K3*RKm3 + K4*RKm4 + K5*RKm5 + K6*RKm6) +
mAK*(K10*RAKm10 + K11*RAKm11 + K12*RAKm12 + K7*RAKm7 + K8*RAKm8 +
K9*RAKm9)*(1 + K2*RAm2 + K3*RAm3 + K4*RAm4 + K5*RAm5 + K6*RAm6)*
(M1 + K10*M10*RKm10 + K11*M11*RKm11 + K12*M12*RKm12 + K2*M2*RKm2 +
K3*M3*RKm3 + K4*M4*RKm4 + K5*M5*RKm5 + K6*M6*RKm6 + K7*M7*RKm7 +
K8*M8*RKm8 + K9*M9*RKm9) =
mKA*(K10*RAKm10 + K11*RAKm11 + K12*RAKm12 + K7*RAKm7 + K8*RAKm8 +
K9*RAKm9)*(M1 + K10*M10*RAm10 + K11*M11*RAm11 + K12*M12*RAm12 +
K2*M2*RAm2 + K3*M3*RAm3 + K4*M4*RAm4 + K5*M5*RAm5 + K6*M6*RAm6 +
K7*M7*RAm7 + K8*M8*RAm8 + K9*M9*RAm9)*
(K10*RKm10 + K11*RKm11 + K12*RKm12 + K7*RKm7 + K8*RKm8 + K9*RKm9) +
mAK*(K10*RAKm10 + K11*RAKm11 + K12*RAKm12 + K7*RAKm7 + K8*RAKm8 +
K9*RAKm9)*(K10*RAm10 + K11*RAm11 + K12*RAm12 + K7*RAm7 + K8*RAm8 +
K9*RAm9)*(M1 + K10*M10*RKm10 + K11*M11*RKm11 + K12*M12*RKm12 +
K2*M2*RKm2 + K3*M3*RKm3 + K4*M4*RKm4 + K5*M5*RKm5 + K6*M6*RKm6 +
K7*M7*RKm7 + K8*M8*RKm8 + K9*M9*RKm9)$
eq11:mLA*(K10*RALm10 + K11*RALm11 + K12*RALm12 + K7*RALm7 + K8*RALm8 + K9*RALm9)*
(M1 + K10*M10*RAm10 + K11*M11*RAm11 + K12*M12*RAm12 + K2*M2*RAm2 +
K3*M3*RAm3 + K4*M4*RAm4 + K5*M5*RAm5 + K6*M6*RAm6 + K7*M7*RAm7 +
K8*M8*RAm8 + K9*M9*RAm9)*
(1 + K2*RLm2 + K3*RLm3 + K4*RLm4 + K5*RLm5 + K6*RLm6) +
mAL*(K10*RALm10 + K11*RALm11 + K12*RALm12 + K7*RALm7 + K8*RALm8 +
K9*RALm9)*(1 + K2*RAm2 + K3*RAm3 + K4*RAm4 + K5*RAm5 + K6*RAm6)*
(M1 + K10*M10*RLm10 + K11*M11*RLm11 + K12*M12*RLm12 + K2*M2*RLm2 +
K3*M3*RLm3 + K4*M4*RLm4 + K5*M5*RLm5 + K6*M6*RLm6 + K7*M7*RLm7 +
K8*M8*RLm8 + K9*M9*RLm9) =
mLA*(K10*RALm10 + K11*RALm11 + K12*RALm12 + K7*RALm7 + K8*RALm8 +
K9*RALm9)*(M1 + K10*M10*RAm10 + K11*M11*RAm11 + K12*M12*RAm12 +
K2*M2*RAm2 + K3*M3*RAm3 + K4*M4*RAm4 + K5*M5*RAm5 + K6*M6*RAm6 +
K7*M7*RAm7 + K8*M8*RAm8 + K9*M9*RAm9)*
(K10*RLm10 + K11*RLm11 + K12*RLm12 + K7*RLm7 + K8*RLm8 + K9*RLm9) +
mAL*(K10*RALm10 + K11*RALm11 + K12*RALm12 + K7*RALm7 + K8*RALm8 +
K9*RALm9)*(K10*RAm10 + K11*RAm11 + K12*RAm12 + K7*RAm7 + K8*RAm8 +
K9*RAm9)*(M1 + K10*M10*RLm10 + K11*M11*RLm11 + K12*M12*RLm12 +
K2*M2*RLm2 + K3*M3*RLm3 + K4*M4*RLm4 + K5*M5*RLm5 + K6*M6*RLm6 +
K7*M7*RLm7 + K8*M8*RLm8 + K9*M9*RLm9)$
sol:solve([eq1,eq2,eq3,eq4,eq5,eq6,eq7,eq8,eq9,eq10,eq11],[K2,K3,K4,K5,K6,K7,K8,K9,K10,K11])$
Here are the missing infos about my system.
wxMaxima version: 17.05.0
Maxima version: 5.40.0
Maxima build date: 2017-06-01 18:54:32
Host type: x86_64-w64-mingw32
System type:
gcc -mno-cygwin -g -O2 -W -Wswitch -Wcomment -Wpointer-arith -Wimplicit -Wreturn-type -Wmissing-declarations -Wno-sign-compare -Wno-format-nonliteral -O2 -fexpensive-optimizations -falign-functions=4 -D_WIN32 -DENABLE_UNICODE -I/usr/local/include -DDYNAMIC_FFI -I. -L/usr/local/lib -lintl /usr/local/lib/libreadline.dll.a -L/usr/local/lib -ltermcap /usr/local/lib/libavcall.a /usr/local/lib/libcallback.a -luser32 -lws2_32 -lole32 -loleaut32 -luuid -liconv -L/usr/local/lib -lsigsegv libgnu_cl.a
SAFETY=0 HEAPCODES STANDARD_HEAPCODES GENERATIONAL_GC SPVW_BLOCKS SPVW_MIXED TRIVIALMAP_MEMORY
libsigsegv 2.8
libiconv 1.13
libreadline 6.0 GNU C 3.4.5 (mingw-vista special r3) PC/386
Lisp implementation type: CLISP
Lisp implementation version: 2.49 (2010-07-07) (built on toshiba [192.168.43.206])
This seems to me like heap exhaustion. Using the :lisp directive from my comment above, you can investigate the current heap size in the underlying Lisp. This is implementation-specific, but assuming you're running on SBCL, the following would retrieve the heap size:
:lisp (cl-user::dynamic-space-size)
Now, Maxima recognizes an environment variable MAXIMA_LISP_OPTIONS, which is just a list of command line parameters passed to Lisp. In SBCL there's a parameter --dynamic-space-size, which specifies the heap size in megabytes. So by running Maxima as follows:
MAXIMA_LISP_OPTIONS="--dynamic-space-size 10000" maxima
you should run the underlying SBCL with 10 GB of heap space, which you can verify as above. This approach would have to be appropriately modified for other Lisp implementations. Let me know if this allows your calculations to run to completion.
I have changed a line in the maxima.bat file.
There you can find some thing like
if exist "%maxima_prefix%/bin/libgcc_s_seh-1.dll" (
if "%lisp_options%"=="" set lisp_options=--dynamic-space-size^ 200
)
I have changed the 200 MB to 8000 MB, this help me to increase the heap size but still I was not able to solve my system of non-linear equations.
"<eventNotification>" +
"<url>" +
Tyc.Website.Properties.Settings.Default.DocusignStatusAPIUrl +
"</url>" +
"<loggingEnabled>" +
true +
"</loggingEnabled>" +
"<requireAcknowledgment>" +
true +
"</requireAcknowledgment>" +
"<includeDocuments>" +
true +
"</includeDocuments>" +
"<EnvelopeEvents>" +
"<envelopeEvent>" +
"<envelopeEventStatusCode>" + "Completed" + "</envelopeEventStatusCode>" +
"<includeDocuments>" + true + "</includeDocuments>" +
"</envelopeEvent>" +
"<envelopeEvent>" +
"<envelopeEventStatusCode>" + "Sent" + "</envelopeEventStatusCode>" +
"<includeDocuments>" + true + "</includeDocuments>" +
"</envelopeEvent>" +
"<envelopeEvent>" +
"<envelopeEventStatusCode>" + "Delivered" + "</envelopeEventStatusCode>" +
"<includeDocuments>" + true + "</includeDocuments>" +
"</envelopeEvent>" +
"<envelopeEvent>" +
"<envelopeEventStatusCode>" + "Sent" + "</envelopeEventStatusCode>" +
"<includeDocuments>" + true + "</includeDocuments>" +
"</envelopeEvent>" +
"<envelopeEvent>" +
"<envelopeEventStatusCode>" + "Sent" + "</envelopeEventStatusCode>" +
"<includeDocuments>" + true + "</includeDocuments>" +
"</envelopeEvent>" +
"</EnvelopeEvents>" +
"<RecipientEvents>" +
"<recipientEvent>" +
"<includeDocuments>" + true + "</includeDocuments>" +
"<recipientEventStatusCode>" + "Sent" + "</recipientEventStatusCode>" +
"</recipientEvent>" +
"<recipientEvent>" +
"<includeDocuments>" + true + "</includeDocuments>" +
"<recipientEventStatusCode>" + "Delivered" + "</recipientEventStatusCode>" +
"</recipientEvent>" +
"<recipientEvent>" +
"<includeDocuments>" + true + "</includeDocuments>" +
"<recipientEventStatusCode>" + "Completed" + "</recipientEventStatusCode>" +
"</recipientEvent>" +
"<recipientEvent>" +
"<includeDocuments>" + true + "</includeDocuments>" +
"<recipientEventStatusCode>" + "AutoResponded" + "</recipientEventStatusCode>" +
"</recipientEvent>" +
"</RecipientEvents>" +
"</eventNotification>"
I use the above request body for docusign event notification. I also tried instead of and am able to get status updates for envelope events but i am not receiving status updates for recipient events. What am i missing here?
I am trying to prove an equation given in the CLRS exercise book. The equation is:
Sigma k=0 to k=infinity (k-1)/2^k = 0
I solved the LHS but my answer is 1 whereas the RHS should be 0
Following is my solution:
Let's say S = k/2^k = 1/2 + 2/2^2 + 3/2^3 + 4/2^4 ....
2S = 1 + 2/2 + 3/2^2 + 4/2^3 ...
2S - S = 1 + ( 2/2 - 1/2) + (3/2^2 - 2/2^2) + (4/2^3 - 3/2^3)..
S = 1+ 1/2 + 1/2^2 + 1/2^3 + 1/2^4..
S = 2 -- eq 1
Now let's say S1 = (k-1)/2^k = 0/2 + 1/2^2 + 2/2^3 + 3/2^4...
S - S1 = 1/2 + (2/2^2 - 1/2^2) + (3/2^3 - 2/2^3) + (4/2^4 - 3/2^4)....
S - S1 = 1/2 + 1/2^2 + 1/2^3 + 1/2^4...
= 1
From eq 1
2 - S1 = 1
S1 = 1
Whereas the required RHS is 0. Is there anything wrong with my solution? Thanks..
Yes, you have issues in your solution to the problem.
While everything is correct in formulating the value of S, you have calculated the value of S1 incorrectly. You missed substituting the value for k=0 in S1. Whereas, for S, even after putting the value of k, the first term will be 0, so no effect.
Therefore,
S1 = (k-1)/2^k = -1 + 0/2 + 1/2^2 + 2/2^3 + 3/2^4...
// you missed -1 here because you started substituting values from k=1
S - S1 = -(-1) + 1/2 + (2/2^2 - 1/2^2) + (3/2^3 - 2/2^3) + (4/2^4 - 3/2^4)....
S - S1 = 1 + (1/2 + 1/2^2 + 1/2^3 + 1/2^4...)
= 1 + 1
= 2.
From eq 1
2 - S1 = 2
S1 = 0.
I have this function which concatenates two matrices:
out->_11 = MAT_MUL(b->_11, a->_11) + MAT_MUL(b->_21, a->_12) + MAT_MUL(b->_31, a->_13) + MAT_MUL(b->_41, a->_14);
out->_12 = MAT_MUL(b->_12, a->_11) + MAT_MUL(b->_22, a->_12) + MAT_MUL(b->_32, a->_13) + MAT_MUL(b->_42, a->_14);
out->_13 = MAT_MUL(b->_13, a->_11) + MAT_MUL(b->_23, a->_12) + MAT_MUL(b->_33, a->_13) + MAT_MUL(b->_43, a->_14);
out->_14 = MAT_MUL(b->_14, a->_11) + MAT_MUL(b->_24, a->_12) + MAT_MUL(b->_34, a->_13) + MAT_MUL(b->_44, a->_14);
out->_21 = MAT_MUL(b->_11, a->_21) + MAT_MUL(b->_21, a->_22) + MAT_MUL(b->_31, a->_23) + MAT_MUL(b->_41, a->_24);
out->_22 = MAT_MUL(b->_12, a->_21) + MAT_MUL(b->_22, a->_22) + MAT_MUL(b->_32, a->_23) + MAT_MUL(b->_42, a->_24);
out->_23 = MAT_MUL(b->_13, a->_21) + MAT_MUL(b->_23, a->_22) + MAT_MUL(b->_33, a->_23) + MAT_MUL(b->_43, a->_24);
out->_24 = MAT_MUL(b->_14, a->_21) + MAT_MUL(b->_24, a->_22) + MAT_MUL(b->_34, a->_23) + MAT_MUL(b->_44, a->_24);
out->_31 = MAT_MUL(b->_11, a->_31) + MAT_MUL(b->_21, a->_32) + MAT_MUL(b->_31, a->_33) + MAT_MUL(b->_41, a->_34);
out->_32 = MAT_MUL(b->_12, a->_31) + MAT_MUL(b->_22, a->_32) + MAT_MUL(b->_32, a->_33) + MAT_MUL(b->_42, a->_34);
out->_33 = MAT_MUL(b->_13, a->_31) + MAT_MUL(b->_23, a->_32) + MAT_MUL(b->_33, a->_33) + MAT_MUL(b->_43, a->_34);
out->_34 = MAT_MUL(b->_14, a->_31) + MAT_MUL(b->_24, a->_32) + MAT_MUL(b->_34, a->_33) + MAT_MUL(b->_44, a->_34);
out->_41 = MAT_MUL(b->_11, a->_41) + MAT_MUL(b->_21, a->_42) + MAT_MUL(b->_31, a->_43) + MAT_MUL(b->_41, a->_44);
out->_42 = MAT_MUL(b->_12, a->_41) + MAT_MUL(b->_22, a->_42) + MAT_MUL(b->_32, a->_43) + MAT_MUL(b->_42, a->_44);
out->_43 = MAT_MUL(b->_13, a->_41) + MAT_MUL(b->_23, a->_42) + MAT_MUL(b->_33, a->_43) + MAT_MUL(b->_43, a->_44);
out->_44 = MAT_MUL(b->_14, a->_41) + MAT_MUL(b->_24, a->_42) + MAT_MUL(b->_34, a->_43) + MAT_MUL(b->_44, a->_44);
MAT_MUL looks like this:
#define MAT_MUL(o1,o2) ((GLfixed)((long)(o1)*(long)(o2))>>16)
The odd thing is that it doesn't work with fixed point values but with float values (MAT_MUL(o1,o2) (o1)*(o2) in this case). I traced the error down to this bit of code.
Any ideas? Thanks
I used to split my Xcode window to 4 sub windows (not popup). I wonder if there's shortcut key to move cursor from one sub window to another ?
+++++++++++++++++++++++++++++
+ + + +
+ G / + F1 + F2 +
+ r F + + +
+ o i +++++++++++++++++++++++
+ u l + + +
+ p e + F3 + F4 +
+ + + +
+++++++++++++++++++++++++++++