QEPCAD Version B 1.72
https://www.usna.edu/Users/cs/wcbrown/qepcad/B/QEPCAD.html
上記の通り,更新されていましたので,インストールスクリプトをUPします.
export CAS=~/CAS mkdir $CAS export qe=$CAS/qesource export saclib=$CAS/saclib2.2.7 cd $CAS wget https://www.usna.edu/Users/cs/wcbrown/qepcad/INSTALL/saclib2.2.7.tar.gz tar zxvf ./saclib2.2.7.tar.gz -C ./ cd $saclib/bin ./sconf ./mkproto ./mkmake ./mklib all cd $CAS wget https://www.usna.edu/Users/cs/wcbrown/qepcad/INSTALL/qepcad-B.1.72.tar.gz tar zxvf ./qepcad-B.1.72.tar.gz -C ./ cd $qe sed -i "s/csh/sh/g" $qe/Makefile make sed -i "s/\#SINGULAR/SINGULAR/g" $qe/default.qepcadrc cd $CAS wget https://www.usna.edu/Users/cs/wcbrown/qepcad/SLFQ/simplify-1.20.tar.gz tar zxvf ./simplify-1.20.tar.gz -C ./ cd ./simplify make sudo ln -s $CAS/qesource/bin/qepcad /usr/local/bin/qepcad sudo ln -s $CAS/simplify/slfq /usr/local/bin/slfq
実行例(1)
echo -e "[] \n (a,b,x,y) \n 2 \n (Ex)(Ey)[x^2+y^2<=1 /\ a x+b y=1]. \n finish" | qepcad
======================================================= Quantifier Elimination in Elementary Algebra and Geometry by Partial Cylindrical Algebraic Decomposition Version B 1.72, Sun Mar 18 22:49:08 EDT 2018 by Hoon Hong (hhong@math.ncsu.edu) With contributions by: Christopher W. Brown, George E. Collins, Mark J. Encarnacion, Jeremy R. Johnson Werner Krandick, Richard Liska, Scott McCallum, Nicolas Robidoux, and Stanly Steinberg ======================================================= Enter an informal description between '[' and ']': []Enter a variable list: (a,b,x,y)Enter the number of free variables: 2 Enter a prenex formula: (Ex)(Ey)[x^2+y^2<=1 /\ a x+b y=1]. ======================================================= Before Normalization > finish An equivalent quantifier-free formula: b^2 + a^2 - 1 >= 0 ===================== The End ======================= ----------------------------------------------------------------------------- 0 Garbage collections, 0 Cells and 0 Arrays reclaimed, in 0 milliseconds. 334662 Cells in AVAIL, 500000 Cells in SPACE. System time: 31 milliseconds. System time after the initialization: 17 milliseconds. -----------------------------------------------------------------------------
実行例(2)
echo -e "[] \n (a,b,x,y) \n 2 \n (Ex)(Ey)[x^4+y^3<=1 /\ a x+b y=1]. \n finish" | qepcad +L100000 +N10000000
======================================================= Quantifier Elimination in Elementary Algebra and Geometry by Partial Cylindrical Algebraic Decomposition Version B 1.72, Sun Mar 18 22:49:08 EDT 2018 by Hoon Hong (hhong@math.ncsu.edu) With contributions by: Christopher W. Brown, George E. Collins, Mark J. Encarnacion, Jeremy R. Johnson Werner Krandick, Richard Liska, Scott McCallum, Nicolas Robidoux, and Stanly Steinberg ======================================================= Enter an informal description between '[' and ']': []Enter a variable list: (a,b,x,y)Enter the number of free variables: 2 Enter a prenex formula: (Ex)(Ey)[x^4+y^3<=1 /\ a x+b y=1]. ======================================================= Before Normalization > finish An equivalent quantifier-free formula: a^8 + 6 a^4 - 3 > 0 \/ 256 b^12 - 768 b^9 + 1728 a^4 b^6 + 768 b^6 - 432 a^8 b^3 + 432 a^4 b^3 - 256 b^3 + 27 a^12 - 54 a^8 + 27 a^4 > 0 \/ [ b > 0 /\ 256 b^12 - 768 b^9 + 1728 a^4 b^6 + 768 b^6 - 432 a^8 b^3 + 432 a^4 b^3 - 256 b^3 + 27 a^12 - 54 a^8 + 27 a^4 = 0 ] ===================== The End ======================= ----------------------------------------------------------------------------- 638 Garbage collections, -1442980436 Cells and 12 Arrays reclaimed, in 25548 milliseconds. 881113 Cells in AVAIL, 5000000 Cells in SPACE. System time: 205804 milliseconds. System time after the initialization: 205697 milliseconds. -----------------------------------------------------------------------------