try: import numpy as np has_numpy = True except ImportError: import math has_numpy = False try: import scipy.constants has_scipy = True except ImportError: has_scipy = False import operator as op from .similar import sim, nsim, gsim, lsim def equation_extend(core): def product(*args): if len(args) == 1 and has_numpy: return np.prod(args[0]) else: return reduce(op.mul,args,1) def sumargs(*args): if len(args) == 1: return sum(args[0]) else: return sum(args) core.addOp('+',"({0:s} + {1:s})","\\left({0:s} + {1:s}\\right)",False,3,op.add) core.addOp('-',"({0:s} - {1:s})","\\left({0:s} - {1:s}\\right)",False,3,op.sub) core.addOp('*',"({0:s} * {1:s})","\\left({0:s} \\times {1:s}\\right)",False,2,op.mul) core.addOp('/',"({0:s} / {1:s})","\\frac{{{0:s}}}{{{1:s}}}",False,2,op.truediv) core.addOp('%',"({0:s} % {1:s})","\\left({0:s} \\bmod {1:s}\\right)",False,2,op.mod) core.addOp('^',"({0:s} ^ {1:s})","{0:s}^{{{1:s}}}",False,1,op.pow) core.addOp('**',"({0:s} ^ {1:s})","{0:s}^{{{1:s}}}",False,1,op.pow) core.addOp('&',"({0:s} & {1:s})","\\left({0:s} \\land {1:s}\\right)",False,4,op.and_) core.addOp('|',"({0:s} | {1:s})","\\left({0:s} \\lor {1:s}\\right)",False,4,op.or_) core.addOp('',"({0:s} {1:s})","\\left({0:s} \\oplus {1:s}\\right)",False,4,op.xor) core.addOp('&|',"({0:s} {1:s})","\\left({0:s} \\oplus {1:s}\\right)",False,4,op.xor) core.addOp('|&',"({0:s} {1:s})","\\left({0:s} \\oplus {1:s}\\right)",False,4,op.xor) core.addOp('==',"({0:s} == {1:s})","\\left({0:s} = {1:s}\\right)",False,5,op.eq) core.addOp('=',"({0:s} == {1:s})","\\left({0:s} = {1:s}\\right)",False,5,op.eq) core.addOp('~',"({0:s} ~ {1:s})","\\left({0:s} \\approx {1:s}\\right)",False,5,sim) core.addOp('!~',"({0:s} !~ {1:s})","\\left({0:s} \\not\\approx {1:s}\\right)",False,5,nsim) core.addOp('!=',"({0:s} != {1:s})","\\left({0:s} \\neg {1:s}\\right)",False,5,op.ne) core.addOp('<>',"({0:s} != {1:s})","\\left({0:s} \\neg {1:s}\\right)",False,5,op.ne) core.addOp('><',"({0:s} != {1:s})","\\left({0:s} \\neg {1:s}\\right)",False,5,op.ne) core.addOp('<',"({0:s} < {1:s})","\\left({0:s} < {1:s}\\right)",False,5,op.lt) core.addOp('>',"({0:s} > {1:s})","\\left({0:s} > {1:s}\\right)",False,5,op.gt) core.addOp('<=',"({0:s} <= {1:s})","\\left({0:s} \\leq {1:s}\\right)",False,5,op.le) core.addOp('>=',"({0:s} >= {1:s})","\\left({0:s} \\geq {1:s}\\right)",False,5,op.ge) core.addOp('=<',"({0:s} <= {1:s})","\\left({0:s} \\leq {1:s}\\right)",False,5,op.le) core.addOp('=>',"({0:s} >= {1:s})","\\left({0:s} \\geq {1:s}\\right)",False,5,op.ge) core.addOp('<~',"({0:s} <~ {1:s})","\\left({0:s} \lessapprox {1:s}\\right)",False,5,lsim) core.addOp('>~',"({0:s} >~ {1:s})","\\left({0:s} \\gtrapprox {1:s}\\right)",False,5,gsim) core.addOp('~<',"({0:s} <~ {1:s})","\\left({0:s} \lessapprox {1:s}\\right)",False,5,lsim) core.addOp('~>',"({0:s} >~ {1:s})","\\left({0:s} \\gtrapprox {1:s}\\right)",False,5,gsim) core.addUnaryOp('!',"(!{0:s})","\\neg{0:s}",op.not_) core.addUnaryOp('-',"-{0:s}","-{0:s}",op.neg) core.addFn('abs',"abs({0:s})","\\left|{0:s}\\right|",1,op.abs) core.addFn('sum',"sum({0:s})","\\sum\\left({0:s}\\right)",'+',sumargs) core.addFn('prod',"prod({0:s})","\\prod\\left({0:s}\\right)",'+',product) if has_numpy: core.addFn('floor',"floor({0:s})","\\lfloor {0:s} \\rfloor",1,np.floor) core.addFn('ceil',"ceil({0:s})","\\lceil {0:s} \\rceil",1,np.ceil) core.addFn('round',"round({0:s})","\\lfloor {0:s} \\rceil",1,np.round) core.addFn('sin',"sin({0:s})","\\sin\\left({0:s}\\right)",1,np.sin) core.addFn('cos',"cos({0:s})","\\cos\\left({0:s}\\right)",1,np.cos) core.addFn('tan',"tan({0:s})","\\tan\\left({0:s}\\right)",1,np.tan) core.addFn('re',"re({0:s})","\\Re\\left({0:s}\\right)",1,np.real) core.addFn('im',"re({0:s})","\\Im\\left({0:s}\\right)",1,np.imag) core.addFn('sqrt',"sqrt({0:s})","\\sqrt{{{0:s}}}",1,np.sqrt) core.addConst("pi",np.pi) core.addConst("e",np.e) core.addConst("Inf",np.Inf) core.addConst("NaN",np.NaN) else: core.addFn('floor',"floor({0:s})","\\lfloor {0:s} \\rfloor",1,math.floor) core.addFn('ceil',"ceil({0:s})","\\lceil {0:s} \\rceil",1,math.ceil) core.addFn('round',"round({0:s})","\\lfloor {0:s} \\rceil",1,round) core.addFn('sin',"sin({0:s})","\\sin\\left({0:s}\\right)",1,math.sin) core.addFn('cos',"cos({0:s})","\\cos\\left({0:s}\\right)",1,math.cos) core.addFn('tan',"tan({0:s})","\\tan\\left({0:s}\\right)",1,math.tan) core.addFn('re',"re({0:s})","\\Re\\left({0:s}\\right)",1,complex.real) core.addFn('im',"re({0:s})","\\Im\\left({0:s}\\right)",1,complex.imag) core.addFn('sqrt',"sqrt({0:s})","\\sqrt{{{0:s}}}",1,math.sqrt) core.addConst("pi",math.pi) core.addConst("e",math.e) core.addConst("Inf",float("Inf")) core.addConst("NaN",float("NaN")) if has_scipy: core.addConst("h",scipy.constants.h) core.addConst("hbar",scipy.constants.hbar) core.addConst("m_e",scipy.constants.m_e) core.addConst("m_p",scipy.constants.m_p) core.addConst("m_n",scipy.constants.m_n) core.addConst("c",scipy.constants.c) core.addConst("N_A",scipy.constants.N_A) core.addConst("mu_0",scipy.constants.mu_0) core.addConst("eps_0",scipy.constants.epsilon_0) core.addConst("k",scipy.constants.k) core.addConst("G",scipy.constants.G) core.addConst("g",scipy.constants.g) core.addConst("q",scipy.constants.e) core.addConst("R",scipy.constants.R) core.addConst("sigma",scipy.constants.e) core.addConst("Rb",scipy.constants.Rydberg)