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.logic import CartExp
from proveit.numbers import Complex, Exp, Interval, Mult, e, i, one, pi, subtract, two, zero
from proveit.physics.quantum import NumKet, QubitSpace, ket1
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
expr = ExprTuple(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))), TensorProd(QubitSpace, CartExp(Complex, two_pow_t)))

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(\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), \mathbb{C}^{2} {\otimes} \mathbb{C}^{2^{t}}\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: 6
2	Operation	operator: 25 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameter: 45 body: 10
7	Operation	operator: 12 operands: 11
8	Operation	operator: 12 operands: 13
9	ExprTuple	45
10	Conditional	value: 14 condition: 15
11	ExprTuple	16, 52
12	Literal
13	ExprTuple	16, 46
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operands: 20
16	Literal
17	Literal
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	45, 23
21	Operation	operator: 48 operands: 24
22	Operation	operator: 25 operands: 26
23	Operation	operator: 27 operands: 28
24	ExprTuple	29, 30
25	Literal
26	ExprTuple	31, 32
27	Literal
28	ExprTuple	33, 34
29	Literal
30	Operation	operator: 35 operands: 36
31	Operation	operator: 37 operand: 54
32	Operation	operator: 38 operands: 39
33	Literal
34	Operation	operator: 40 operands: 41
35	Literal
36	ExprTuple	52, 42, 43, 44, 45
37	Literal
38	Literal
39	ExprTuple	45, 53
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