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, t
from proveit.linear_algebra import ScalarMult, TensorProd, VecSum
from proveit.numbers import Exp, Interval, Mult, e, i, one, pi, subtract, two, zero
from proveit.physics.quantum import NumKet, ket1
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
expr = ExprTuple(Exp(e, Mult(two, pi, i, _phase, two_pow_t)), VecSum(index_or_indices = [k], summand = ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), 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())

\left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot 2^{t}}, \sum_{k=0}^{2^{t} - 1} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \left(\lvert 1 \rangle {\otimes} \lvert k \rangle_{t}\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: 44 operands: 3
2	Operation	operator: 4 operand: 7
3	ExprTuple	25, 6
4	Literal
5	ExprTuple	7
6	Operation	operator: 31 operands: 8
7	Lambda	parameter: 41 body: 10
8	ExprTuple	48, 38, 39, 40, 42
9	ExprTuple	41
10	Conditional	value: 11 condition: 12
11	Operation	operator: 13 operands: 14
12	Operation	operator: 15 operands: 16
13	Literal
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	41, 19
17	Operation	operator: 44 operands: 20
18	Operation	operator: 21 operands: 22
19	Operation	operator: 23 operands: 24
20	ExprTuple	25, 26
21	Literal
22	ExprTuple	27, 28
23	Literal
24	ExprTuple	29, 30
25	Literal
26	Operation	operator: 31 operands: 32
27	Operation	operator: 33 operand: 50
28	Operation	operator: 34 operands: 35
29	Literal
30	Operation	operator: 36 operands: 37
31	Literal
32	ExprTuple	48, 38, 39, 40, 41
33	Literal
34	Literal
35	ExprTuple	41, 49
36	Literal
37	ExprTuple	42, 43
38	Literal
39	Literal
40	Literal
41	Variable
42	Operation	operator: 44 operands: 45
43	Operation	operator: 46 operand: 50
44	Literal
45	ExprTuple	48, 49
46	Literal
47	ExprTuple	50
48	Literal
49	Variable
50	Literal