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, VecAdd, VecSum
from proveit.numbers import Exp, Interval, Mult, e, i, one, pi, subtract, two, zero
from proveit.physics.quantum import NumKet, ket0, ket1
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
expr = ExprTuple(VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, _phase, two_pow_t)), ket1)), VecSum(index_or_indices = [k], summand = ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), 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(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot 2^{t}} \cdot \lvert 1 \rangle\right), \sum_{k=0}^{2^{t} - 1} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle_{t}\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 operands: 4
2	Operation	operator: 5 operand: 9
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9
7	Operation	operator: 19 operand: 36
8	Operation	operator: 20 operands: 11
9	Lambda	parameter: 45 body: 13
10	ExprTuple	36
11	ExprTuple	14, 15
12	ExprTuple	45
13	Conditional	value: 16 condition: 17
14	Operation	operator: 48 operands: 18
15	Operation	operator: 19 operand: 54
16	Operation	operator: 20 operands: 21
17	Operation	operator: 22 operands: 23
18	ExprTuple	34, 24
19	Literal
20	Literal
21	ExprTuple	25, 26
22	Literal
23	ExprTuple	45, 27
24	Operation	operator: 38 operands: 28
25	Operation	operator: 48 operands: 29
26	Operation	operator: 30 operands: 31
27	Operation	operator: 32 operands: 33
28	ExprTuple	52, 42, 43, 44, 46
29	ExprTuple	34, 35
30	Literal
31	ExprTuple	45, 53
32	Literal
33	ExprTuple	36, 37
34	Literal
35	Operation	operator: 38 operands: 39
36	Literal
37	Operation	operator: 40 operands: 41
38	Literal
39	ExprTuple	52, 42, 43, 44, 45
40	Literal
41	ExprTuple	46, 47
42	Literal
43	Literal
44	Literal
45	Variable
46	Operation	operator: 48 operands: 49
47	Operation	operator: 50 operand: 54
48	Literal
49	ExprTuple	52, 53
50	Literal
51	ExprTuple	54
52	Literal
53	Variable
54	Literal