Expression of type ScalarMult

from the theory of proveit.linear_algebra.scalar_multiplication

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.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Function, c, k
from proveit.core_expr_types import Q__b_1_to_j, b_1_to_j, f__b_1_to_j
from proveit.linear_algebra import ScalarMult, VecSum

# build up the expression from sub-expressions
sub_expr1 = [b_1_to_j]
expr = ScalarMult(k, VecSum(index_or_indices = sub_expr1, summand = ScalarMult(Function(c, sub_expr1), f__b_1_to_j), condition = Q__b_1_to_j))

expr:

# 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

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

k \cdot \left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~\left(c\left(b_{1}, b_{2}, \ldots, b_{j}\right) \cdot f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right)\right]

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 10 operands: 1
1	ExprTuple	2, 3
2	Variable
3	Operation	operator: 4 operand: 6
4	Literal
5	ExprTuple	6
6	Lambda	parameters: 17 body: 7
7	Conditional	value: 8 condition: 9
8	Operation	operator: 10 operands: 11
9	Operation	operator: 12 operands: 17
10	Literal
11	ExprTuple	13, 14
12	Variable
13	Operation	operator: 15 operands: 17
14	Operation	operator: 16 operands: 17
15	Variable
16	Variable
17	ExprTuple	18
18	ExprRange	lambda_map: 19 start_index: 20 end_index: 21
19	Lambda	parameter: 25 body: 22
20	Literal
21	Variable
22	IndexedVar	variable: 23 index: 25
23	Variable
24	ExprTuple	25
25	Variable