# from the theory of proveit.numbers.multiplication¶

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
# import Expression classes needed to build the expression
from proveit import ExprRange, ExprTuple, IndexedVar, Variable, b, j
from proveit.core_expr_types import a_1_to_i, b_1_to_j, c_1_to_k
from proveit.numbers import Add, Mult, one

In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
expr = ExprTuple(Mult(a_1_to_i, Add(b_1_to_j), c_1_to_k), Add(ExprRange(sub_expr1, Mult(a_1_to_i, IndexedVar(b, sub_expr1), c_1_to_k), one, j)))

expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot \left(b_{1} +  b_{2} +  \ldots +  b_{j}\right)\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}, \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot b_{1}\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\right) +  \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot b_{2}\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\right) +  \ldots +  \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot b_{j}\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\right)\right)

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
wrap_positionsposition(s) at which wrapping is to occur; 'n' is after the nth comma.()()('with_wrapping_at',)
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'leftleft('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0ExprTuple1, 2
1Operationoperator: 14
operands: 3
2Operationoperator: 7
operands: 4
3ExprTuple17, 5, 19
4ExprTuple6
5Operationoperator: 7
operands: 8
6ExprRangelambda_map: 9
start_index: 25
end_index: 13
7Literal
8ExprTuple10
9Lambdaparameter: 28
body: 11
10ExprRangelambda_map: 12
start_index: 25
end_index: 13
11Operationoperator: 14
operands: 15
12Lambdaparameter: 33
body: 16
13Variable
14Literal
15ExprTuple17, 18, 19
16IndexedVarvariable: 22
index: 33
17ExprRangelambda_map: 20
start_index: 25
end_index: 21
18IndexedVarvariable: 22
index: 28
19ExprRangelambda_map: 24
start_index: 25
end_index: 26
20Lambdaparameter: 33
body: 27
21Variable
22Variable
23ExprTuple28
24Lambdaparameter: 33
body: 29
25Literal
26Variable
27IndexedVarvariable: 30
index: 33
28Variable
29IndexedVarvariable: 31
index: 33
30Variable
31Variable
32ExprTuple33
33Variable