|
62 | 62 | "SymEngine.ascii_art"
|
63 | 63 | ]
|
64 | 64 | },
|
| 65 | + { |
| 66 | + "cell_type": "markdown", |
| 67 | + "metadata": {}, |
| 68 | + "source": [ |
| 69 | + "or create a variable" |
| 70 | + ] |
| 71 | + }, |
| 72 | + { |
| 73 | + "cell_type": "code", |
| 74 | + "execution_count": 3, |
| 75 | + "metadata": { |
| 76 | + "collapsed": false |
| 77 | + }, |
| 78 | + "outputs": [ |
| 79 | + { |
| 80 | + "data": { |
| 81 | + "text/plain": [ |
| 82 | + "#<SymEngine::Basic:0x00000001e95290>" |
| 83 | + ] |
| 84 | + }, |
| 85 | + "execution_count": 3, |
| 86 | + "metadata": {}, |
| 87 | + "output_type": "execute_result" |
| 88 | + } |
| 89 | + ], |
| 90 | + "source": [ |
| 91 | + "basic = SymEngine::Basic.new" |
| 92 | + ] |
| 93 | + }, |
65 | 94 | {
|
66 | 95 | "cell_type": "markdown",
|
67 | 96 | "metadata": {},
|
|
585 | 614 | "source": [
|
586 | 615 | "k.expand.to_s"
|
587 | 616 | ]
|
588 |
| - }, |
589 |
| - { |
590 |
| - "cell_type": "markdown", |
591 |
| - "metadata": {}, |
592 |
| - "source": [ |
593 |
| - "## SymEngine::RealDouble\n", |
594 |
| - "\n", |
595 |
| - "SymEngine::RealDouble can be constructed by converting any ruby Float into SymEngine" |
596 |
| - ] |
597 |
| - }, |
598 |
| - { |
599 |
| - "cell_type": "code", |
600 |
| - "execution_count": null, |
601 |
| - "metadata": { |
602 |
| - "collapsed": true |
603 |
| - }, |
604 |
| - "outputs": [], |
605 |
| - "source": [ |
606 |
| - "d = SymEngine(1.2)" |
607 |
| - ] |
608 |
| - }, |
609 |
| - { |
610 |
| - "cell_type": "markdown", |
611 |
| - "metadata": {}, |
612 |
| - "source": [ |
613 |
| - "## SymEngine::ComplexDouble\n", |
614 |
| - "SymEngine::ComplexDouble can be constructed by converting any ruby Complex into SymEngine" |
615 |
| - ] |
616 |
| - }, |
617 |
| - { |
618 |
| - "cell_type": "code", |
619 |
| - "execution_count": null, |
620 |
| - "metadata": { |
621 |
| - "collapsed": true |
622 |
| - }, |
623 |
| - "outputs": [], |
624 |
| - "source": [ |
625 |
| - "c = SymEngine(Complex(2.3, 3.2))" |
626 |
| - ] |
627 |
| - }, |
628 |
| - { |
629 |
| - "cell_type": "markdown", |
630 |
| - "metadata": {}, |
631 |
| - "source": [ |
632 |
| - "## SymEngine::RealMPFR\n", |
633 |
| - "SymEngine::RealMPFR can be constructed either by converting any Ruby BigDecimal into SymEngine, or using the constructor to express any real number with a given number of bits of precision" |
634 |
| - ] |
635 |
| - }, |
636 |
| - { |
637 |
| - "cell_type": "code", |
638 |
| - "execution_count": null, |
639 |
| - "metadata": { |
640 |
| - "collapsed": true |
641 |
| - }, |
642 |
| - "outputs": [], |
643 |
| - "source": [ |
644 |
| - "require 'bigdecimal'\n", |
645 |
| - "r1 = SymEngine(BigDecimal(\"12.3\"))\n", |
646 |
| - "r2 = SymEngine::RealMPFR.new(12.3, 200)" |
647 |
| - ] |
648 |
| - }, |
649 |
| - { |
650 |
| - "cell_type": "markdown", |
651 |
| - "metadata": {}, |
652 |
| - "source": [ |
653 |
| - "## SymEngine::ComplexMPC\n", |
654 |
| - "SymEngine::RealMPC can be constructed by arithmatic operations of any SymEngine::RealMPFR objects, as shown below." |
655 |
| - ] |
656 |
| - }, |
657 |
| - { |
658 |
| - "cell_type": "code", |
659 |
| - "execution_count": null, |
660 |
| - "metadata": { |
661 |
| - "collapsed": true |
662 |
| - }, |
663 |
| - "outputs": [], |
664 |
| - "source": [ |
665 |
| - "i = SymEngine:I\n", |
666 |
| - "c1 = r1 + i * r2" |
667 |
| - ] |
668 |
| - }, |
669 |
| - { |
670 |
| - "cell_type": "markdown", |
671 |
| - "metadata": {}, |
672 |
| - "source": [ |
673 |
| - "## SymEngine::Constant - SymEngine Constants\n", |
674 |
| - "\n", |
675 |
| - "SymEngine offers the following constants" |
676 |
| - ] |
677 |
| - }, |
678 |
| - { |
679 |
| - "cell_type": "code", |
680 |
| - "execution_count": null, |
681 |
| - "metadata": { |
682 |
| - "collapsed": true |
683 |
| - }, |
684 |
| - "outputs": [], |
685 |
| - "source": [ |
686 |
| - "i = SymEngine::I\n", |
687 |
| - "e = SymEngine::E\n", |
688 |
| - "eg = SymEngine::EULER_GAMMA\n", |
689 |
| - "pi = SymEngine::PI\n", |
690 |
| - "\n", |
691 |
| - "i.inspect + e.inspect + eg.inspect + pi.inspect" |
692 |
| - ] |
693 |
| - }, |
694 |
| - { |
695 |
| - "cell_type": "markdown", |
696 |
| - "metadata": {}, |
697 |
| - "source": [ |
698 |
| - "## SymEngine::TrigFunction\n", |
699 |
| - "\n", |
700 |
| - "sin, cos, tan, cosec, sec, cot, asin, acos, atan, acosec, asec, acot are available as shown below:" |
701 |
| - ] |
702 |
| - }, |
703 |
| - { |
704 |
| - "cell_type": "code", |
705 |
| - "execution_count": null, |
706 |
| - "metadata": { |
707 |
| - "collapsed": true |
708 |
| - }, |
709 |
| - "outputs": [], |
710 |
| - "source": [ |
711 |
| - "i1 = SymEngine::sin(pi)\n", |
712 |
| - "i2 = SymEngine::cos(0.2)\n", |
713 |
| - "i3 = SymEngine::tan(pi/4)\n", |
714 |
| - "i4 = SymEngine::csc(pi/2)\n", |
715 |
| - "i5 = SymEngine::sec(0.2)\n", |
716 |
| - "i6 = SymEngine::cot(pi/4)\n", |
717 |
| - "\n", |
718 |
| - "print \"sin(pi): \", i1,\"\\ncos(0.2): \", i2, \"\\ntan(pi/4): \", i3, \"\\ncsc(pi/2): \", i4, \"\\nsec(0.2): \", i5,\"\\ncot(pi/4): \", i6, \"\\n\"" |
719 |
| - ] |
720 |
| - }, |
721 |
| - { |
722 |
| - "cell_type": "code", |
723 |
| - "execution_count": null, |
724 |
| - "metadata": { |
725 |
| - "collapsed": true |
726 |
| - }, |
727 |
| - "outputs": [], |
728 |
| - "source": [ |
729 |
| - "i1 = SymEngine::asin(1)\n", |
730 |
| - "i2 = SymEngine::acos(0)\n", |
731 |
| - "i3 = SymEngine::atan(5)\n", |
732 |
| - "i4 = SymEngine::acsc(1)\n", |
733 |
| - "i5 = SymEngine::asec(0.2)\n", |
734 |
| - "i6 = SymEngine::acot(0.5)\n", |
735 |
| - "\n", |
736 |
| - "print \"i1: \", i1,\"\\ni2: \", i2, \"\\ni3: \", i3, \"\\ni4: \", i4, \"\\ni5: \", i5,\"\\ni6: \", i6, \"\\n\"" |
737 |
| - ] |
738 |
| - }, |
739 |
| - { |
740 |
| - "cell_type": "markdown", |
741 |
| - "metadata": {}, |
742 |
| - "source": [ |
743 |
| - "## SymEngine::HyperbolicFunction\n", |
744 |
| - "sinh, cosh, tanh, cosech, sech, coth, asinh, acosh, atanh, acosech, asech, acoth are available as shown below:" |
745 |
| - ] |
746 |
| - }, |
747 |
| - { |
748 |
| - "cell_type": "code", |
749 |
| - "execution_count": null, |
750 |
| - "metadata": { |
751 |
| - "collapsed": true |
752 |
| - }, |
753 |
| - "outputs": [], |
754 |
| - "source": [ |
755 |
| - "i1 = SymEngine::sinh(pi)\n", |
756 |
| - "i2 = SymEngine::cosh(0.2)\n", |
757 |
| - "i3 = SymEngine::tanh(pi/4)\n", |
758 |
| - "i4 = SymEngine::csch(pi/2)\n", |
759 |
| - "i5 = SymEngine::sech(0.2)\n", |
760 |
| - "i6 = SymEngine::coth(pi/4)\n", |
761 |
| - "\n", |
762 |
| - "print \"sinh(pi): \", i1,\"\\ncosh(0.2): \", i2, \"\\ntanh(pi/4): \", i3, \"\\ncsch(pi/2): \", i4, \"\\nsech(0.2): \", i5,\"\\ncoth(pi/4): \", i6, \"\\n\"" |
763 |
| - ] |
764 |
| - }, |
765 |
| - { |
766 |
| - "cell_type": "code", |
767 |
| - "execution_count": null, |
768 |
| - "metadata": { |
769 |
| - "collapsed": true |
770 |
| - }, |
771 |
| - "outputs": [], |
772 |
| - "source": [ |
773 |
| - "i1 = SymEngine::asinh(1)\n", |
774 |
| - "i2 = SymEngine::acosh(0)\n", |
775 |
| - "i3 = SymEngine::atanh(5)\n", |
776 |
| - "i4 = SymEngine::acsch(1)\n", |
777 |
| - "i5 = SymEngine::asech(0.2)\n", |
778 |
| - "i6 = SymEngine::acoth(0.5)\n", |
779 |
| - "\n", |
780 |
| - "print \"i1: \", i1,\"\\ni2: \", i2, \"\\ni3: \", i3, \"\\ni4: \", i4, \"\\ni5: \", i5,\"\\ni6: \", i6, \"\\n\"" |
781 |
| - ] |
782 |
| - }, |
783 |
| - { |
784 |
| - "cell_type": "markdown", |
785 |
| - "metadata": {}, |
786 |
| - "source": [ |
787 |
| - "## NTheory Functions\n", |
788 |
| - "\n", |
789 |
| - "Several Number Theory functions are available in SymEngine.\n", |
790 |
| - "\n", |
791 |
| - "GCD and LCM" |
792 |
| - ] |
793 |
| - }, |
794 |
| - { |
795 |
| - "cell_type": "code", |
796 |
| - "execution_count": null, |
797 |
| - "metadata": { |
798 |
| - "collapsed": true |
799 |
| - }, |
800 |
| - "outputs": [], |
801 |
| - "source": [ |
802 |
| - "gcd = SymEngine::gcd(45, 40)\n", |
803 |
| - "lcm = SymEngine::lcm(45, 40)\n", |
804 |
| - "\n", |
805 |
| - "print \"for 45 and 40,\\ngcd is: \", gcd, \"\\nlcm is: \",lcm, \"\\n\"" |
806 |
| - ] |
807 |
| - }, |
808 |
| - { |
809 |
| - "cell_type": "markdown", |
810 |
| - "metadata": {}, |
811 |
| - "source": [ |
812 |
| - "Next Prime" |
813 |
| - ] |
814 |
| - }, |
815 |
| - { |
816 |
| - "cell_type": "code", |
817 |
| - "execution_count": null, |
818 |
| - "metadata": { |
819 |
| - "collapsed": true |
820 |
| - }, |
821 |
| - "outputs": [], |
822 |
| - "source": [ |
823 |
| - "np = SymEngine::nextprime(5)" |
824 |
| - ] |
825 |
| - }, |
826 |
| - { |
827 |
| - "cell_type": "markdown", |
828 |
| - "metadata": {}, |
829 |
| - "source": [ |
830 |
| - "Quotient" |
831 |
| - ] |
832 |
| - }, |
833 |
| - { |
834 |
| - "cell_type": "code", |
835 |
| - "execution_count": null, |
836 |
| - "metadata": { |
837 |
| - "collapsed": true |
838 |
| - }, |
839 |
| - "outputs": [], |
840 |
| - "source": [ |
841 |
| - "q = SymEngine::quotient(5, 2)" |
842 |
| - ] |
843 |
| - }, |
844 |
| - { |
845 |
| - "cell_type": "markdown", |
846 |
| - "metadata": {}, |
847 |
| - "source": [ |
848 |
| - "Lucas and Fibonacci series" |
849 |
| - ] |
850 |
| - }, |
851 |
| - { |
852 |
| - "cell_type": "code", |
853 |
| - "execution_count": null, |
854 |
| - "metadata": { |
855 |
| - "collapsed": true |
856 |
| - }, |
857 |
| - "outputs": [], |
858 |
| - "source": [ |
859 |
| - "l = SymEngine::lucas(3)\n", |
860 |
| - "f = SymEngine::fibonacci(3)\n", |
861 |
| - "\n", |
862 |
| - "p l, f" |
863 |
| - ] |
864 |
| - }, |
865 |
| - { |
866 |
| - "cell_type": "markdown", |
867 |
| - "metadata": {}, |
868 |
| - "source": [ |
869 |
| - "Binomials" |
870 |
| - ] |
871 |
| - }, |
872 |
| - { |
873 |
| - "cell_type": "code", |
874 |
| - "execution_count": null, |
875 |
| - "metadata": { |
876 |
| - "collapsed": true |
877 |
| - }, |
878 |
| - "outputs": [], |
879 |
| - "source": [ |
880 |
| - "b = SymEngine::binomial(5, 2)" |
881 |
| - ] |
882 | 617 | }
|
883 | 618 | ],
|
884 | 619 | "metadata": {
|
885 | 620 | "kernelspec": {
|
886 |
| - "display_name": "Ruby 2.3.0", |
| 621 | + "display_name": "Ruby 2.2.0", |
887 | 622 | "language": "ruby",
|
888 | 623 | "name": "ruby"
|
889 | 624 | },
|
|
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