Core Language

Programming with Variable Lengths

UpTo is a symbolic specification that can be used to represent up to a given number of objects or positions. Many functions support this new specification, which makes programming with expressions of variable lengths very easy.

Take up to the first 5 elements of a binary list of unknown size.

In[1]:=
Click for copyable input
list = RandomInteger[1, RandomInteger[{1, 10}]]; Take[list, UpTo[5]]
Out[1]=

Obtain the 6 most common elements of a list, or as many as there are if fewer.

In[2]:=
Click for copyable input
Commonest[{b, a, c, 2, a, b, 1, 2}, UpTo[6]]
Out[2]=

Create a ragged partition into blocks of up to 3 elements long, where the last sublists can be shorter.

In[3]:=
Click for copyable input
Partition[{a, b, c, d, e, f, g}, UpTo[3]]
Out[3]=
In[4]:=
Click for copyable input
Partition[{a, b, c, d, e, f, g}, UpTo[3], 1]
Out[4]=

Partition an image so that lengths are up to 36 pixels and heights are up to 28 pixels.

In[5]:=
Click for copyable input
img = \!\(\* GraphicsBox[ TagBox[RasterBox[CompressedData[" 1:eJxc2gVQnOm6Luw9aybuLpCEGAnx4O6ugeDu7tJIu7u70o07jbu7uxOSQITY ZGzNsln7nI/M2rv+/6RuvmoCqaS46n7e54VcD0/xCP/+v/7rv/KANx7wtvea LE/iVoHzW4mlfdyaMVnjTEnbUnXPWuPAi7bhV10j2z2jOz0jO91D2139Lzu6 XzS1ryublyuVc4UVk5KiEY6sj8xrQ1OU2Yii+AxOQCTK0TPJyM7vnomdir7R aW2dw1paB7W0D+roHjY0PmFhfdbO6ZKTm4qr55VnvlefB173DbkZEH47KOpO WLxGVMqDxKwnaXlamTCdXLQ+DG+EJplhKGY4mjmRacPgOQmk7kWlQa1NicM9 ubPDyPkxzPwYFnjOjCCnhuATg5DR/tyR/uzRIcjwGGJ0EjU+gx2fw4/P40YX cSPL+KEV/MAqtncN1bYGa96AdLzG9r2jDn/kTn6Vzf1avPzXqvW/N2z9s+31 Hz1v/t3/9r8H3/730Jt/D+z80ffqn50v/tay/lv98s/Vcz+WjO9Ke14xWlbQ DbPg6vG00v4YRXuwpMFHUOXBLnKhiOywLCsU1QJBNgfjTUAYo0y0SRrKOAll Eo8yjUaZRWLMI7GW4QSbOIZTCsclieWczHTOZLvmcD3gQi+izI+mCGAo/Bn5 fsx8P5bcn10QyK+KlrenlQ7mVU+i6ufxzSu0tg1250tB97a4d0fKKAcJGzGF 3YzKYVH9dFHbYnU3wLfVPvSNb2SnF8jwTvfA647ureaO9fo9vtmiiglp4SBX 1k3mt2JodRBUaTJIEBKLd/PLMHMKeWzqdE3X+Iy27lEt7UOaWoc0tQ9p6RzU 0TtsYHrc3PaMjdMFR/fLrj5XPALVvENv+keqB8ffi0h7FJejmQrXBWENwSQT 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Out[5]=
In[6]:=
Click for copyable input
ImagePartition[img, {UpTo[36], UpTo[28]}] // Grid
Out[6]=

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