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Expression of type Equals

from the theory of proveit.physics.quantum.QPE

In [1]:
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 ExprRange, Variable, e, l
from proveit.core_expr_types import Len
from proveit.logic import Equals
from proveit.numbers import Add, Exp, Interval, Sum, frac, one, subtract, two
from proveit.physics.quantum.QPE import _two_pow__t_minus_one
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Sum(index_or_indices = [l], summand = frac(one, Exp(l, two)), domain = Interval(Add(e, one), subtract(_two_pow__t_minus_one, one)))
expr = Equals(Len(operands = [sub_expr2, sub_expr2]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, two)]))
expr:
In [3]:
# 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
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
|\left(\sum_{l = e + 1}^{2^{t - 1} - 1} \frac{1}{l^{2}}, \sum_{l = e + 1}^{2^{t - 1} - 1} \frac{1}{l^{2}}\right)| = |\left(1, \ldots, 2\right)|
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 6
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8, 8
6Literal
7ExprTuple9
8Operationoperator: 10
operand: 13
9ExprRangelambda_map: 12
start_index: 46
end_index: 38
10Literal
11ExprTuple13
12Lambdaparameter: 17
body: 17
13Lambdaparameter: 29
body: 16
14ExprTuple17
15ExprTuple29
16Conditionalvalue: 18
condition: 19
17Variable
18Operationoperator: 20
operands: 21
19Operationoperator: 22
operands: 23
20Literal
21ExprTuple46, 24
22Literal
23ExprTuple29, 25
24Operationoperator: 36
operands: 26
25Operationoperator: 27
operands: 28
26ExprTuple29, 38
27Literal
28ExprTuple30, 31
29Variable
30Operationoperator: 40
operands: 32
31Operationoperator: 40
operands: 33
32ExprTuple34, 46
33ExprTuple35, 43
34Variable
35Operationoperator: 36
operands: 37
36Literal
37ExprTuple38, 39
38Literal
39Operationoperator: 40
operands: 41
40Literal
41ExprTuple42, 43
42Literal
43Operationoperator: 44
operand: 46
44Literal
45ExprTuple46
46Literal