Expression of type VecSum

from the theory of proveit.physics.quantum.QPE

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, Variable, k, t
from proveit.linear_algebra import ScalarMult, TensorProd, VecSum
from proveit.numbers import Interval, one, subtract, zero
from proveit.physics.quantum import NumKet, ket1
from proveit.physics.quantum.QPE import two_pow_t

# build up the expression from sub-expressions
sub_expr1 = [k]
expr = VecSum(index_or_indices = sub_expr1, summand = ScalarMult(Function(Variable("_a", latex_format = r"{_{-}a}"), sub_expr1), TensorProd(ket1, NumKet(k, t))), domain = Interval(zero, subtract(two_pow_t, one)))

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())

\sum_{k=0}^{2^{t} - 1} \left({_{-}a}\left(k\right) \cdot \left(\lvert 1 \rangle {\otimes} \lvert k \rangle_{t}\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameter: 29 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	29, 13
11	Operation	operator: 14 operand: 29
12	Operation	operator: 16 operands: 17
13	Operation	operator: 18 operands: 19
14	Variable
15	ExprTuple	29
16	Literal
17	ExprTuple	20, 21
18	Literal
19	ExprTuple	22, 23
20	Operation	operator: 24 operand: 38
21	Operation	operator: 25 operands: 26
22	Literal
23	Operation	operator: 27 operands: 28
24	Literal
25	Literal
26	ExprTuple	29, 37
27	Literal
28	ExprTuple	30, 31
29	Variable
30	Operation	operator: 32 operands: 33
31	Operation	operator: 34 operand: 38
32	Literal
33	ExprTuple	36, 37
34	Literal
35	ExprTuple	38
36	Literal
37	Variable
38	Literal