# 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 ExprTuple, Function, Q, f
from proveit.core_expr_types import a_1_to_i, b_1_to_j, c_1_to_k
from proveit.numbers import Mult, Sum
from proveit.numbers.summation import summation_b1toj_fQ

In [2]:
# build up the expression from sub-expressions
sub_expr1 = [b_1_to_j]
expr = ExprTuple(Mult(a_1_to_i, summation_b1toj_fQ, c_1_to_k), Sum(index_or_indices = sub_expr1, summand = Mult(a_1_to_i, Function(f, sub_expr1), c_1_to_k), condition = Function(Q, sub_expr1)))

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[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right]\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}, \sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\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: 13
operands: 3
2Operationoperator: 7
operand: 6
3ExprTuple16, 5, 18
4ExprTuple6
5Operationoperator: 7
operand: 10
6Lambdaparameters: 23
body: 9
7Literal
8ExprTuple10
9Conditionalvalue: 11
condition: 15
10Lambdaparameters: 23
body: 12
11Operationoperator: 13
operands: 14
12Conditionalvalue: 17
condition: 15
13Literal
14ExprTuple16, 17, 18
15Operationoperator: 19
operands: 23
16ExprRangelambda_map: 20
start_index: 31
end_index: 21
17Operationoperator: 22
operands: 23
18ExprRangelambda_map: 24
start_index: 31
end_index: 25
19Variable
20Lambdaparameter: 37
body: 26
21Variable
22Variable
23ExprTuple27
24Lambdaparameter: 37
body: 28
25Variable
26IndexedVarvariable: 29
index: 37
27ExprRangelambda_map: 30
start_index: 31
end_index: 32
28IndexedVarvariable: 33
index: 37
29Variable
30Lambdaparameter: 37
body: 34
31Literal
32Variable
33Variable
34IndexedVarvariable: 35
index: 37
35Variable
36ExprTuple37
37Variable