1 | initial version |

Here is one way to use a colormap with your plots.

In this example, we set the number of curves, and run through the colormap in that many steps.

```
sage: cm = colormaps.Blues
sage: n = 20
sage: color = lambda j: cm(floor(j*255/n))[:3]
sage: Terms = [x^(2+j)*(2+(-1)^(j+1)) for j in range(n)]
sage: Sums = [sum(Terms[0:n]) for n in range(n)]
sage: Figures = [plot(Sums[j], (x, -1.2, 1.2), ymin=-3, ymax = 3, color=color(j)) for j in range(n)]
sage: f = sum(Figures)
sage: f.show()
```

2 | No.2 Revision |

Here is one way to use a colormap with your plots.

In this example, we set the number of curves, and run through the colormap in that many steps.

```
sage: cm = colormaps.Blues
sage:
```~~n ~~nmax = 20
sage: color = lambda j: ~~cm(floor(j*255/n))[:3]
~~cm(floor(j*255/nmax))[:3]
sage: Terms = [x^(2+j)*(2+(-1)^(j+1)) for j in ~~range(n)]
~~range(nmax)]
sage: Sums = [sum(Terms[0:n]) for n in ~~range(n)]
~~range(nmax)]
sage: Figures = [plot(Sums[j], (x, -1.2, 1.2), ymin=-3, ~~ymax = 3, ~~ymax=3, color=color(j)) for j in ~~range(n)]
~~range(nmax)]
sage: f = sum(Figures)
sage: f.show()

3 | No.3 Revision |

Here is one way to use a colormap with your plots.

In this example, we set the number of curves, and run through the colormap in that many steps.

```
sage: cm = colormaps.Blues
sage: nmax = 20
sage: color = lambda j: cm(floor(j*255/nmax))[:3]
sage: Terms = [x^(2+j)*(2+(-1)^(j+1)) for j in range(nmax)]
sage: Sums = [sum(Terms[0:n]) for n in range(nmax)]
sage: Figures = [plot(Sums[j], (x, -1.2, 1.2), ymin=-3, ymax=3, color=color(j)) for j in range(nmax)]
sage: f = sum(Figures)
sage: f.show()
```

**Edit.** (To answer follow-up question in the comment.)

Colormaps have 256 levels numbered 0 to 255,
so `color`

above maps [0 .. nmax - 1] into [0 .. 255].

To leave out the first half of the colormap, use instead:

```
sage: color = lambda j: cm(floor(128 + j*127/nmax))[:3]
```

or if you want to go nonlinearly using some function `h`

from [0 .. nmax-1] to the interval [0, 1], just use

```
sage: color = lambda j: cm(floor(255*h(j))[:3]
```

(That looks better indeed.)

The reason for `[:3]`

is that a colormap returns four values,
corresponding to R, G, B and opacity (also known as alpha),
but typically opacity is 1.0 throughout (since most colormaps
do not play with transparency).

To further refine the above and make the transition through
colors more continuous, instead of using `cm(floor(...))`

one
could use the fractional part of `255*h(j)`

to move gradually
between the colors at `floor(255*h(j))`

and `ceil(255*h(j))`

in the colormap... (Not clear one could perceive the effect
of that though!)

To do that, given a function `h`

as above, you could do

```
def color(j):
h = RR(255*h(j))
r0, g0, b0 = cm(h.floor())[:3] # rgb at floor
r1, g1, b1 = cm(h.ceil())[:3] # rgb at ceiling
f = h.frac() # fractional part
r = (1-f) * r0 + f * r1
g = (1-f) * g0 + f * g1
b = (1-f) * b0 + f * b1
return r, g, b
```

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