def EC_nf_plot(E,base_field_gen_name):
K = E.base_field()
n1 = K.signature()[0]
if n1 == 0:
return plot([])
prec = 53
maxprec = 10**6
while prec < maxprec: # Try to base change to R. May fail if resulting curve is almost singular, so increase precision.
try:
SR = K.embeddings(RealField(prec))
X = [E.base_extend(s) for s in SR]
break
except ArithmeticError:
prec *= 2
if prec >= maxprec:
return text("Unable to plot",(1,1),fontsize="xx-large")
X = [e.plot() for e in X]
xmin = min([x.xmin() for x in X])
xmax = max([x.xmax() for x in X])
ymin = min([x.ymin() for x in X])
ymax = max([x.ymax() for x in X])
cols = ["blue","red","green","orange","brown"] # Preset colours, because rainbow tends to return too pale ones
if n1 > len(cols):
cols = rainbow(n1)
return sum([EC_R_plot([SR[i](a) for a in E.ainvs()],xmin,xmax,ymin,ymax,cols[i],"$"+base_field_gen_name+" \mapsto$ "+str(SR[i].im_gens()[0].n(20))) for i in range(n1)])
def EC_nf_plot(K, ainvs, base_field_gen_name):
try:
n1 = K.signature()[0]
if n1 == 0:
return plot([])
R=[]
S=K.embeddings(RDF)
for s in S:
A=[s(c) for c in ainvs]
R.append(EC_R_plot_zone(Rx([A[4],A[3],A[1],1]),Rx([A[2],A[0]])))
xmin = min([r[0] for r in R])
xmax = max([r[1] for r in R])
ymin = min([r[2] for r in R])
ymax = max([r[3] for r in R])
cols = rainbow(n1) # Default choice of n colours
# However, these tend to be too pale, so we preset them for small values of n
if n1==1:
cols=["blue"]
elif n1==2:
cols=["red","blue"]
elif n1==3:
cols=["red","limegreen","blue"]
elif n1==4:
cols = ["red", "orange", "forestgreen", "blue"]
elif n1==5:
cols = ["red", "orange", "forestgreen", "blue", "darkviolet"]
elif n1==6:
cols = ["red", "darkorange", "gold", "forestgreen", "blue", "darkviolet"]
elif n1==7:
cols = ["red", "darkorange", "gold", "forestgreen", "blue", "darkviolet", "fuchsia"]
return sum([EC_R_plot([S[i](c) for c in ainvs], xmin, xmax, ymin, ymax, cols[i], "$" + base_field_gen_name + " \mapsto$ " + str(S[i].im_gens()[0].n(20))+"$\dots$") for i in range(n1)])
except:
return text("Unable to plot", (1, 1), fontsize=36)
def EC_nf_plot(K, ainvs, base_field_gen_name):
try:
n1 = K.signature()[0]
if n1 == 0:
return plot([])
R=[]
S=K.embeddings(RDF)
for s in S:
A=[s(c) for c in ainvs]
R.append(EC_R_plot_zone(Rx([A[4],A[3],A[1],1]),Rx([A[2],A[0]])))
xmin = min([r[0] for r in R])
xmax = max([r[1] for r in R])
ymin = min([r[2] for r in R])
ymax = max([r[3] for r in R])
cols = rainbow(n1) # Default choice of n colours
# However, these tend to be too pale, so we preset them for small values of n
if n1==1:
cols=["blue"]
elif n1==2:
cols=["red","blue"]
elif n1==3:
cols=["red","limegreen","blue"]
elif n1==4:
cols = ["red", "orange", "forestgreen", "blue"]
elif n1==5:
cols = ["red", "orange", "forestgreen", "blue", "darkviolet"]
elif n1==6:
cols = ["red", "darkorange", "gold", "forestgreen", "blue", "darkviolet"]
elif n1==7:
cols = ["red", "darkorange", "gold", "forestgreen", "blue", "darkviolet", "fuchsia"]
return sum([EC_R_plot([S[i](c) for c in ainvs], xmin, xmax, ymin, ymax, cols[i], "$" + base_field_gen_name + " \mapsto$ " + str(S[i].im_gens()[0].n(20))+"$\dots$") for i in range(n1)])
except:
return text("Unable to plot", (1, 1), fontsize=36)
def EC_nf_plot(E, base_field_gen_name):
K = E.base_field()
n1 = K.signature()[0]
if n1 == 0:
return plot([])
prec = 53
maxprec = 10 ** 6
while prec < maxprec: # Try to base change to R. May fail if resulting curve is almost singular, so increase precision.
try:
SR = K.embeddings(RealField(prec))
X = [E.base_extend(s) for s in SR]
break
except ArithmeticError:
prec *= 2
if prec >= maxprec:
return text("Unable to plot", (1, 1), fontsize="xx-large")
X = [e.plot() for e in X]
xmin = min([x.xmin() for x in X])
xmax = max([x.xmax() for x in X])
ymin = min([x.ymin() for x in X])
ymax = max([x.ymax() for x in X])
cols = ["blue", "red", "green", "orange", "brown"] # Preset colours, because rainbow tends to return too pale ones
if n1 > len(cols):
cols = rainbow(n1)
return sum([EC_R_plot([SR[i](a) for a in E.ainvs()], xmin, xmax, ymin, ymax, cols[i], "$" + base_field_gen_name + " \mapsto$ " + str(SR[i].im_gens()[0].n(20))) for i in range(n1)])
def EC_nf_plot(E,base_field_gen_name):
K = E.base_field()
SR = K.embeddings(RR)
n1 = len(SR)
if n1 == 0:
return plot([])
X = [E.base_extend(s).plot() for s in SR]
xmin = min([x.xmin() for x in X])
xmax = max([x.xmax() for x in X])
ymin = min([x.ymin() for x in X])
ymax = max([x.ymax() for x in X])
cols = rainbow(n1)
return sum([EC_R_plot([SR[i](a) for a in E.ainvs()],xmin,xmax,ymin,ymax,cols[i],"$"+base_field_gen_name+" \mapsto$ "+str(SR[i].im_gens()[0].n(20))) for i in range(n1)])
def EC_nf_plot(E, base_field_gen_name):
K = E.base_field()
SR = K.embeddings(RR)
n1 = len(SR)
if n1 == 0:
return plot([])
X = [E.base_extend(s).plot() for s in SR]
xmin = min([x.xmin() for x in X])
xmax = max([x.xmax() for x in X])
ymin = min([x.ymin() for x in X])
ymax = max([x.ymax() for x in X])
cols = rainbow(n1)
return sum([
EC_R_plot([SR[i](a) for a in E.ainvs()], xmin, xmax, ymin, ymax,
cols[i], "$" + base_field_gen_name + " \mapsto$ " +
str(SR[i].im_gens()[0].n(20))) for i in range(n1)
])
def EC_nf_plot(E, base_field_gen_name):
K = E.base_field()
n1 = K.signature()[0]
if n1 == 0:
return plot([])
prec = 53
maxprec = 10 ** 6
while prec < maxprec: # Try to base change to RR. May fail if resulting curve is almost singular, so increase precision.
try:
SR = K.embeddings(RealField(prec))
X = [E.base_extend(s) for s in SR]
break
except ArithmeticError:
prec *= 2
if prec >= maxprec:
return text("Unable to plot", (1, 1), fontsize=36)
try:
X = [e.plot() for e in X]
except:
return text("Unable to plot", (1, 1), fontsize=36)
xmin = min([x.xmin() for x in X])
xmax = max([x.xmax() for x in X])
ymin = min([x.ymin() for x in X])
ymax = max([x.ymax() for x in X])
cols = rainbow(n1) # Default choice of n colours
# Howver, these tend to be too pale, so we preset them for small values of n
if n1==1:
cols=["blue"]
elif n1==2:
cols=["red","blue"]
elif n1==3:
cols=["red","limegreen","blue"]
elif n1==4:
cols = ["red", "orange", "forestgreen", "blue"]
elif n1==5:
cols = ["red", "orange", "forestgreen", "blue", "darkviolet"]
elif n1==6:
cols = ["red", "darkorange", "gold", "forestgreen", "blue", "darkviolet"]
elif n1==7:
cols = ["red", "darkorange", "gold", "forestgreen", "blue", "darkviolet", "fuchsia"]
return sum([EC_R_plot([SR[i](a) for a in E.ainvs()], xmin, xmax, ymin, ymax, cols[i], "$" + base_field_gen_name + " \mapsto$ " + str(SR[i].im_gens()[0].n(20))+"$\dots$") for i in range(n1)])
def EC_nf_plot(E, base_field_gen_name):
K = E.base_field()
n1 = K.signature()[0]
if n1 == 0:
return plot([])
prec = 53
maxprec = 10 ** 6
while prec < maxprec: # Try to base change to RR. May fail if resulting curve is almost singular, so increase precision.
try:
SR = K.embeddings(RealField(prec))
X = [E.base_extend(s) for s in SR]
break
except ArithmeticError:
prec *= 2
if prec >= maxprec:
return text("Unable to plot", (1, 1), fontsize="xx-large")
X = [e.plot() for e in X]
xmin = min([x.xmin() for x in X])
xmax = max([x.xmax() for x in X])
ymin = min([x.ymin() for x in X])
ymax = max([x.ymax() for x in X])
cols = rainbow(n1) # Default choice of n colours
# Howver, these tend to be too pale, so we preset them for small values of n
if n1==1:
cols=["blue"]
elif n1==2:
cols=["red","blue"]
elif n1==3:
cols=["red","limegreen","blue"]
elif n1==4:
cols = ["red", "orange", "forestgreen", "blue"]
elif n1==5:
cols = ["red", "orange", "forestgreen", "blue", "darkviolet"]
elif n1==6:
cols = ["red", "darkorange", "gold", "forestgreen", "blue", "darkviolet"]
elif n1==7:
cols = ["red", "darkorange", "gold", "forestgreen", "blue", "darkviolet", "fuchsia"]
return sum([EC_R_plot([SR[i](a) for a in E.ainvs()], xmin, xmax, ymin, ymax, cols[i], "$" + base_field_gen_name + " \mapsto$ " + str(SR[i].im_gens()[0].n(20))+"$\dots$") for i in range(n1)])