Hi
Ubuntu 18.04 Jupyter notebook SageMath 9.0
Q1):
I can't find why the first time I click on r or on t buttons it produces 2 rotations or 2 reflections, then only one as it should do, every other time.(maybe there is something wrong in my code ? ) (to enlarge the output cell, menu cell -> Current output → toggle scrolling and click on left side of the output cell)
Q2):
why this code do not work on SageCell ?
or is there a bug in interact button ? https://ask.sagemath.org/question/48338/interact-button-reacting-twice/
#%matplotlib notebook
#import matplotlib.pyplot as plt
#from matplotlib.animation import FuncAnimation
#import animatplot as amp
#
import numpy as np
from scipy.spatial import distance
from sage.plot.point import Point
#np.set_printoptions(linewidth=110)
""" choose side number of the 2D polygon """
var('n')
n=6
maL=[]
shiftAngle=-2*pi/(2*n)
for i in range(1,n+1) :
maL.append([cos(i*2*pi/n+shiftAngle),sin(i*2*pi/n+shiftAngle)])
#mL=[[1,1],[-1,1],[-1,-1],[1,-1]]
m=matrix(maL).transpose()
max = 1.5 # figure span
figsizeV=5
def chooseColor(colorsNumber):
if 'colorL' not in locals():
colorL=[]
for i in range(0,colorsNumber) :
colorL.append([random(),random(),random()])
#show(colorL)
D=distance.cdist(colorL, colorL, 'cityblock')
Dm=matrix(D)
DvL=[]
for v in (Dm.columns()):
DvL.append((sum(v)))
#show(DvL)
keys = range(len(DvL))
DvDict=dict(zip(DvL, keys))
#show(DvDict)
DvDictSorted={k: v for k, v in sorted(DvDict.items(), key=lambda item: item[0],reverse=True)}
#show(DvDictSorted)
colorSortedL=[]
for key,val in DvDictSorted.items():
colorSortedL.append(colorL[val])
#print (key, "=>", val)
return colorSortedL
rot=matrix(SR,[[cos(2*pi/n),-sin(2*pi/n)],[sin(2*pi/n),cos(2*pi/n)]])
#ref=matrix(SR,[[cos(2*2*pi/n),sin(2*2*pi/n)],[sin(2*2*pi/n),-cos(2*2*pi/n)]])
ref=matrix(SR,[[cos(pi),sin(pi)],[sin(pi),-cos(pi)]])
# fill up color list only if color list does not exist
try: colorSortedL
except NameError: colorSortedL = None
if colorSortedL ==None :
colorSortedL=chooseColor(2*n)
#print("https://www.youtube.com/watch?v=L5GEnUuhilw&t=204s")
#show(LatexExpr(r"\mathrm{rotation_{matrix}} = \begin{bmatrix}\cos{2\pi \over n} & -\sin{2\pi \over n} \\[8pt] \sin{2\pi \over n} & \cos{2\pi \over n}\end{bmatrix} "))
#show(LatexExpr(r"\mathrm{reflexion_{matrix}} = \left(\begin{array}{rr} \cos 2 \theta & \sin 2 \theta \\ \
# \sin 2 \theta & -\cos 2 \theta \end{array}\right)"))
#show("rotation Matrix :\t",rot)
#show("reflexion Matrix :\t",ref)
#show(maL)
#show(colorSortedL)
def getRotAndReflexionMatrix(rotAndRefSerie) :
global m
#show(rot,ref)
global rotAndReflexionMatricesL
global rotAndRefMemo
mrt=m
#show("rotAndRefMemo before:\t", rotAndRefMemo,"rotAndRefSerie :\t", rotAndRefSerie)
rotAndRefMemot=deepcopy(deepcopy(rotAndRefMemo) + deepcopy(rotAndRefSerie))
#show("rotAndRefMemo :\t", rotAndRefMemot,"rotAndRefSerie :\t", rotAndRefSerie)
rotAndReflexionMatricesL=[]
for c in rotAndRefMemot :
if c=='r' :
mrt=rot*mrt
rotAndReflexionMatricesL.append(mrt)
elif c=='t' :
mrt=ref*mrt
rotAndReflexionMatricesL.append(mrt)
elif c=='c' :
#clear
mrt=m
rotAndReflexionMatricesL=[m]
rotAndRefMemot=[ ]
else :
#clear
mrt=m
rotAndReflexionMatricesL=[ ]
rotAndRefMemot=[ ]
print("only i or r or t please")
#show("rotAndRefMemo :\t", rotAndRefMemo,"rotAndRefSerie :\t", rotAndRefSerie)
rotAndRefMemo=deepcopy(rotAndRefMemot)
return mrt
def buildMatriceFigPlots(matricesL):
figPlotsL=[]
figPlot=plot(0, ymin=-1.25, ymax=1.25)
for matrice in matricesL :
matriceL=list(matrice.transpose())
figPlot=(list_plot(matriceL,color='black',size=40,figsize=(figsizeV,figsizeV)))
for i in range(0,len(matriceL)) :
#show(matriceL[i])
figPlot+=text(str(i), matriceL[i], fontsize=50, rgbcolor=colorSortedL[i] )
figPlot+= polygon([matriceL[i],matriceL[(i+1)%n],(0,0)],fill=True, thickness=4, rgbcolor=colorSortedL[i])
figPlot += circle((0,0), 1)
#figPlot += polygon(matriceL,fill=False, thickness=4, color='orange')
figPlotsL.append(figPlot)
#for c in range(0,t.dimensions()[1]) :
#for r in range(0,t.dimensions()[0]) :
# show(r,":\t",r,":\t",t[r,c])
return figPlotsL
try: rotAndReflexionMatrix
except NameError: rotAndReflexionMatrix = None
if rotAndReflexionMatrix ==None :
rotAndReflexionMatrix=m
try: rotAndReflexionMatricesL
except NameError: rotAndReflexionMatricesL = None
if rotAndReflexionMatricesL ==None :
rotAndReflexionMatricesL=[]
try: rotAndRefMemo
except NameError: rotAndRefMemo = None
#
if rotAndRefMemo ==None :
rotAndRefMemo=[]
try: matricesFigPlotsL
except NameError: matricesFigPlotsL = None
if matricesFigPlotsL ==None :
matricesFigPlotsL=[]
animateTest=False
from IPython.core.display import display, HTML
#display(HTML("<style>.container { height:100% !important; }</style>"))
display(HTML("<style>.container { width:80% !important; }</style>"))
@interact
def _(aMap=selector(['c','r', 't'],buttons=True)):
rotAndRef=list(aMap)
#show("rotAnd Reflexion sequence: \t",rotAndRef)
global rotAndReflexionMatrix
global rotAndReflexionMatricesL
rotAndReflexionMatrix=getRotAndReflexionMatrix(rotAndRef)
#show("rotAndReflexionMatrix : \t",rotAndReflexionMatrix)
#show("rotAndReflexionMatricesL : \t",rotAndReflexionMatricesL)
# plot list of matrices
matricesFigPlotsL=buildMatriceFigPlots(rotAndReflexionMatricesL)
if animateTest :
# show animated sequence
a=animate(matricesFigPlotsL,ymin=-max,ymax=max,axes_labels=['x','y'],fontsize=14,figsize=(figsizeV,figsizeV))
a.show(delay=200,iterations=1)
else:
#only show the completed sequence at the end
if matricesFigPlotsL!=[] :
show(matricesFigPlotsL[-1])
