Expression of type ExprTuple

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 ExprTuple, k
from proveit.linear_algebra import ScalarMult, VecSum
from proveit.numbers import Exp, Interval, Mult, e, frac, i, one, pi, sqrt, two, zero
from proveit.physics.quantum import Ket
from proveit.physics.quantum.QPE import SubIndexed, _phase, _psi

# build up the expression from sub-expressions
expr = ExprTuple(SubIndexed(_psi, [one]), ScalarMult(frac(one, sqrt(two)), VecSum(index_or_indices = [k], summand = ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), Ket(k)), domain = Interval(zero, 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())

\left(\lvert \psi_{1} \rangle, \frac{1}{\sqrt{2}} \cdot \left(\sum_{k=0}^{1} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle\right)\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 3 operand: 36
2	Operation	operator: 20 operands: 5
3	Literal
4	ExprTuple	36
5	ExprTuple	6, 7
6	Operation	operator: 18 operands: 8
7	Operation	operator: 9 operand: 12
8	ExprTuple	36, 11
9	Literal
10	ExprTuple	12
11	Operation	operator: 27 operands: 13
12	Lambda	parameter: 43 body: 14
13	ExprTuple	39, 15
14	Conditional	value: 16 condition: 17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	Operation	operator: 22 operands: 23
18	Literal
19	ExprTuple	36, 39
20	Literal
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	43, 26
24	Operation	operator: 27 operands: 28
25	Operation	operator: 29 operand: 43
26	Operation	operator: 31 operands: 32
27	Literal
28	ExprTuple	33, 34
29	Literal
30	ExprTuple	43
31	Literal
32	ExprTuple	35, 36
33	Literal
34	Operation	operator: 37 operands: 38
35	Literal
36	Literal
37	Literal
38	ExprTuple	39, 40, 41, 42, 43
39	Literal
40	Literal
41	Literal
42	Literal
43	Variable